Unable to sign out off my Apple Account

If an app or feature on your device is not working, not appearing, or is restricted (grayed out), a frequent reason is it may have been disabled using Screen Time, or by an IT administrator if you are using a device owned by an employer or educational institution.

- Read this support article If your Apple ID or other options are greyed out in Settings —> If your Apple Account is grayed out in Settings - Apple Support

Tap Settings > Screen Time > Content & Privacy > scroll to Allow Changes and turn on.

- If the device is managed (Settings > General > VPN & Device Management), contact the IT department that is doing the managing.

If you see a message telling you to wait before being able to sign in or out, you may need to read this article about Stolen Device Protection: About Stolen Device Protection for iPhone - Apple Support

Try and turn off screen time completely. Most of the times you're able to sign out then, unless, your apple account is managed by a company and the system administration has put restrictions in place