From all the discussion around this, I had the mistaken understanding that all internal links created in the new version always open in the browser, but this is not so. If you copy an internal link (via the Note menu) and paste into another note, then you can click on that note from within Evernote app to go to that note within the app. It does not go to the browser if you pasted the internal link correctly and you clicked on it from within the Evernote app.
If you find that the internal link does open in the browser, then perhaps you are making the mistake that I did, which causes the internal link to get converted to a web link on paste. After copying the link, the mistake is to select text in another note and then use “Add link” via right-click or use the Insert Link button on the toolbar. If you do that, the internal link will get converted to a web link. The key is to stay away from the add/insert link functionality for adding an internal link. Instead, rather than selecting text first, just click into the text (no selection) and paste. What gets pasted is an internal link, and then you can still edit the displayed text like always after it is pasted, but it will not get converted to a web link in this case.
The real difference in behavior at this time is that the old links could open a note in the Evernote app even when accessed outside of the app, but this is not possible to get such links in the new version.