PinkElephant

You did not do enough to REALLY uninstall.
The Macs usual routine does not purge every app component. Get the app AppCleaner from the internet. Install it, use it to remove all program parts. Then restart the Mac.
Install EN again, from the EN website, not the AppStore. Should now open and allow you to log in.

My login works with 1 Password, and I have no issue at all.
Open EN, get the login screen, open 1PW (if it is not already open), and for me (on my Macs) it offers to fill the user ID. I need to choose, I have more than one account,
On enter the password field is showing, same procedure, password fills by itself. Enter again.
If 2FA is enabled, I now need a second app, because IMHO it contradicts TWO factor authentication to have it all in ONE app. So I need to type 6 digits. Enter and done.
EN uses the cloaked password field to avoid a specific type of brute forcing that is called „Spraying“. This method drops a high number of trials on the login pages of the target. To avoid being locked out, they attack a single account only every several minutes, but circulate the attack over many vectors. The classical brute force detection may be outmaneuvered.
The way EN shows the password field only after a valid (!) user name has been entered effectively prevents spraying to be successful. If you are security oriented, you should welcome this move.

@newbie user On a new Free account, there are 5 emails allowed, to demonstrate what would be possible with a subscription. After these 5 emails are send, the service stops on the Free account. So your observation is correct: You could use it initially, and later it stopped working.
This is properly documented, but maybe you have overlooked the notification. That it stops is not a bug, it is intentionally. If you need that feature, subscribing is the way to get it on a permanent basis.

Yes, this seems to be the standard. Says the same in my devices view.
But ok, you are within the devices limit, so it should work.
You can only try to erase the EN website data in the browsers you are using, restart the browser and try again.
As a rule of thumb when switching browsers or devices try to really log out of your account on one before you try to open EN on another.
The other option would be an installed client, but then you loose the web option, since it counts as another device.

Who told to avoid the "&" symbol ?
It is not listed in the search syntax grammar as parameter. On a fast test, tags beginning with & worked as any others. 
Symbols to be avoided are "-", "*" and ":", and maybe some more.

Legacy client (7.14 and before) ?
macOS Ventura ?
Then you are viewing at maybe the first proof that the legacy client will be gone one day. This viewing problem came with the Ventura update, and the legacy client will not be updated to accommodate for it. If not Apple does something on their end, the legacy client will continue to display like it does. EN will not do anything about it, the client is deprecated since 2020.

The only ways to influence this is by a) subscribing (not what I promote, just for completeness) or b) send another support ticket.
Maybe they learn to scale it down when enough paying users complain.

You can't search the same database on 2 different Macs - search happens on the local database on the Mac, not on the cloud.
And this database in the much hyped legacy version can and does collect mistakes.
If I remember it correctly (I did not bother to install legacy on my new Mac), you need to hold down the option-key before opening the help menu. You then get an additional set of options, among them an option to recreate the search index. When you run it, it will take a while crunching through the database. At the end you have a fresh index. Do this on both Macs.
There are more troubleshooting options you can try.
Personally I think the new sync - when released - will eventually kill legacy, because it will change the underlying data structure. So better have your Plan B (I really don't care if it is v10 or something else) ready for execution, just in case.

Maybe set the local databases back on all computers, and download a fresh set of local notes from the server.
This usually does the job on single PCs (slightly different on Macs), but I see no reason that it should not work as well on a Teams account.
Go to File > Sign Out [name] from the menu bar. Select the "Remove my Evernote data from this device" option, then click Sign out. Restart your computer. Sign back in to Evernote. Keep the app open while it downloads your notes from the server.  

If somebody wants to sort "by date" using a field that contains text, the date must be written in a certain sequence. Only YYYYMMDD will properly sort. This is no surprise at all - every text "date" only sorts in that order. It is different if the date field is based on a number - then it sorts by ordering this number. 
If you put the day first DDMMYYYY, it will first sort all 1st of whatever, followed by lowest month, year coming last, then 2nd, then 3rd. Putting the month first, it will sort all Januaries, Februaries etc.
Since there are date fields, one of them editable it makes little sense to type a date into the title field first of all. Personally I warn against modifying the created-date field, because the system may overwrite it again. But who wants to use it may do so.

Maybe it is just a question of the sequence in which extensions are enabled.
My setup is much leaner, most of your adguard stuff is not needed, because it all ends up in my pi hole. In general every extension weakens internet security - even when the devs of the extension claim they enhance it.
If you want to report it to the devs, you need to issue a support ticket.

OK, don't know if this has an effect, but update to 10.50.
Second question: Is this the AppStore version ? If yes, you should switch to the direct download. The AppStore version is the same software, but the Mac executes it in a sandbox. This can have unpredictable side effects - we had plenty of them here in the forum. I use AppCleaner to remove an app - when checking all elements to remove, this will have the effect of downloading a fresh copy of your EN database from the server as well. Just leave the app open for a while until the network traffic indicating an ongoing download stops.
If this solved it, fine. If not, come back.

You did something wrong when switching devices.
The usual procedure is to open your account on any device you want to skip. Log out, and when this is confirmed by a login greeting, close the app.
Then you use the ultimate device / client to go to your account, tab devices and unsync the devices where you logged out before.
You need to be down to the one last device in the devices page before you can add another one.
Most of the time people forget to log out first. Then the still existing login makes EN believe the device is still active. This even happens when the app was uninstalled without logout, or erased for sale or scrap. How should EN know ?
Since there is a cap of 2 unsyncs per 30 days, it can be you already used up your allowed actions. Then it means to wait 30 days, or to subscribe to a month of Personal.

This is a typical sign of a corrupted database. To correct it:
Go to File > Sign Out [name] from the menu bar.  Select the "Remove my Evernote data from this device" option, then click Sign out.
Or use the same option from the app settings, and log out. Restart your computer. Sign back in to Evernote. Keep the app open while it downloads your notes from the server.

Nesting tasks is no option, and if you look at the way tasks were implemented, you understand why we won’t get nested tasks.
To get close to it, you can use a note to hold several tasks, using the note as a project or field of work container for tasks. You can tag the note, which means you can filter for this tag and in addition filter only notes that hold tasks (or open / closed tasks, to be more specific).
For more elaborate task management use a full task manager - to replace them is not the main focus of tasks in EN. Tasks in EN are a tool to make notes actionable, and this it does better than any task manager.

No, the volume of notes won’t be a problem. The system limits have not changed. I think that the install did go wrong at some point.
I would do this: Quit (cmd-Q) the EN app. Uninstall the app, using the app AppCleaner. Make sure all elements are checked for removal - scroll down the list and set the checkbox where it may be missing. Uninstall. Then restart the Mac.
Now get the direct download from the EN website. Install it, open, enter your login data. It should now open regularly. The initial download will go pretty fast, and you can already work with it. It will just not be snappy for some time, because it basically runs on the server, while it downloads your content for local use in the background.
Because of this, leave the EN app open, running in the background - it will continue to build your local database. Depending on your internet speed and Macs power, this can take hours or even days.

Oh, if the app sort of freezes on hitting the checkmark, there is more about it:
https://help.evernote.com/hc/en-us/articles/217930798
Happened to me 2 or 3 times. I copied my notes content, and used Apple Notes as a safe haven. I then killed the app, reopened it and pasted the content back. Then it synced without a problem.
In general there are 2 things we can do more often to keep app and device healthy: Log out of the account in the app from time to time, close it, reopen, log in again. And with the device switching it off maybe once in a week can solve a lot of issues.

I would start with changing my account password from „Evernote123“ to something more adequate …
A little bit of historical review:
The hack in 2013 did NOT compromise login credentials. EN decided as a safety measure to reset all account logins, which later showed to be not necessary - but better safe than sorry (kudos to ENs security team).
There was NO breach in 2020.
There is no breach in 2022 (OK, it’s not over yet, but up to now).
What exists are all sorts of other threats: Weak and reused passwords (user issue), no 2FA enabled (user issue), malware with keyloggers and screengrabbers on users computers, copying login credentials (indirectly a user issue as well). It is in anybodies hands to improve protection against these threats.
And of course there are users who fail in protecting their credentials, do not learn from their deficiencies and continue to blame others, because (of course) it happens to them again and again.

Yes, this problem has been reported already several times from legacy users after upgrading to Ventura.
First 7.14 is the latest version of legacy - which means it will be the latest version of v7 on the Mac forever. It was abandoned 2 years ago when the new version 10 was released. Version 7 is deprecated, it runs as long as it runs, and when it fails, its dead. Now it doesn‘t outright fail, but its use is handicapped.
We can have luck, and the display problem is a side effect of something else, and when Apple changes this „something else“ the app will again display fine. Possible, but IMHO not likely, and for sure nothing to wait for.
So the probable next step will be to migrate to version 10. I would urge you to use the direct download from the EN website, not the version from the AppStore.
If you are using local (not synced) notebooks, they will be migrated to cloud storage in the process. If you want to avoid this, you need to export them first using legacy, and store them on the drive, or any other place. Don‘t use ENEX, because you need an EN client to open this format, and then it would import them into the cloud when you do.
Beside this, the migration takes part, and after it you are back in sync with the apps progress. We have already 48 release cycles of the new app behind us, so take your time to familiarize yourself wit the changes. There is a large series of good videos on the official channel of Evernote on YouTube. And there are several new features that did not exist at all in the legacy versions.

Try to log out of your account in web clipper settings, close the browser, open it, open web clipper and log back in.
This should draw fresh metadata from the server.

Works on the Mac desktop 10.48 as well.
To see how it works: Copy the link, go to the note, double click on a word to select it, right click for a drop down menu, choose "Add link".
In the little box that appears, the first field is filled with the selected word (or words), into the second field insert the link. Hit OK.
That's the long version, where you see every step as you proceed.

This is possible through a filter. Hit the parent tag, and select „include all child tags“. Here an example, even works on mobile, thanks to v10 that brought nesting to the mobile clients.
Since Tags really got a boost with v10, I would rethink the project. Notebooks are not a really good way to organize things in detail. And they are a disaster when looking at it from a workflow perspective.

OK, the API is a different story.
About the 50 notes limit: It is somehow coded into the v10 desktop clients. But it can be raised with a small intervention. I did not get it raised above 1.000, but that’s still a lot. I used to set it to 500. But since it will often be overwritten when updating, I only do it if I want to handle a lot of notes in one go - which happens quite rarely.
And v10 takes longer to process such a large selection, so it is best done in the background while using other programs on the computer.

https://help.evernote.com/hc/en-us/articles/360052801693
Sharing notebooks is not a feature any more.