While I'm glad to have some solution rather than no solution, this is an absurdly low quality quick-fix to the problem. The problem is that the EA app specifically sends a notification to Windows 10/11 that it has been minimized into the system tray rather than closed based on the user preference in settings. No other app sends a notification to the OS about this including Steam, Ubisoft Connect, Epic Games, Battle.Net, etc. so no, it's not mainly handled by Windows.
Your proposed solution to specifically this one app acting different than all other apps in an annoying way to to entirely disable this app's ability to send any notification for any reason indefinitely (or until the setting is reverted to default "On"). This means that the EA app would be unable to notify the user of anything through Windows regardless of the notification. The issue isn't that it is capable of sending notifications. The issue is that it sends this specific one repeatedly in a very annoying way, and no other mainstream app does this.