I need a way to reproduce it. Could you record a short video of the issue? That might give me a clue what I need to do to see the issue myself. From mere screenshots I can not judge how you got there.
EDIT: OK, I see the issue with the missing search field. Seems this has been introduced in the latest iOS16 update. If you can, update to iOS17 which does not have this problem.
Is the correct song displayed if you close and reopen lyrics view?