Cannot sign out of Apple ID.

When I go to Settings>Name> Sign Out nothing happens. I click the button and i get no type of prompt or anything.

Additionally, I can't turn on find my iPhone. When I go to the setting to toggle it on, it toggles on for a second, then if I go back a page it shows "Find My iPhone: Off" again.

I've tried resetting settings. Resetting all content seems to fix the issue but I'd rather not lose all my photos and messages. Backing up and restoring doesn't solve the issue either.

iPhone X

iOS 13.3