For me at least the app works as it should now. Another update, total app re-install may, but probably wont' help.
I understand your frustration. Worst case I'v heard, I would be equally furious.
There is one thing that may be responsible for this. I doubt it but it's worth putting out there.
It's the game. The Sims 2. It seems a lot of people have had problems with that particular game, all sorts of stuff, some of it would be relevant to your huge issue, although no idea if it helps.
If you have any other games on the EA App. Especially something not carried over from origin. It should work. If not then your problem is exactly as you describe - and I would share your sentiments.
15years ago is a while, and there were transition hiccups. Plus The Sims 2 seems to have a variety of issues. If that's your only game on EA_App, after everything you have done so far I doubt you'll solve it without EA direct help, which you should get.
Edit: Silly me. You recently bought The Sims 4. I haven't looked in the Sims 4 thread, but it's the same line of games.
Also you have no access to your account, although you recently bought Sims 4. That should not be the case. And EA_Support, need to assist, you. That's going by what you have written. Could be something else security related, but still, it absolutely should be given attention and solved by EA.