Can't start the game, being asked to reinstall even after reinstalling twice

You will see similar posts throughout EA Forums. You need to install using the launcher for the company you bought the game from - sound like Steam in your case.

Then, you need to always launch from that company's launcher (not directly with EA app).

Your apps may be confused at the moment, so you may need uninstall the game, EA app and Steam and then reinstall Steam and then the game (from Steam).