WORKAROUND!!!
I found a workaround. It does show it is a bit "*****"... Hopefully they will fix it asap...
When clicking on the "Authorize" button on the Evernote for Gmail addon within Gmail, a pop-up window opens to do the actual authorization. During a very brief moment (matter of couple of seconds), the addon itself (on the right of Gmail, not the new pop-up window) is still in mode "waiting"/"thinking" (you see some dynamic action on the frame). After a while, that "dynamic" action stops and the addon is in a more static state.
If you click the Authorize button on the pop-up window once the addon (on the right of GMail) has stopped, then you have the error: Token Mismatch (I guess the dynamic frame is kinda showing some timeout that, once passed (hence the dynamic action stops), the Evernote addon cancels the token on its side).
Well, if you are able to be the fastest "clicker" in the old wild western of internet... and click on Authorize (on the po-up window) before that dynamic action on the add-on frame stops, the authorization seems to be succesful. At least it worked on my side.
Now, once linked, you can do stuff on the add-on, but I am noticing that the add-on is PAINFULLY slow... 😞
So again, @mi_cha, what will be your replacement apps/workflow? Really interested. Thanks!