Windows 11 has a sort of a bug with the taskbar when using multiple monitors (atleast in dual monitor setups) where if you have the start menu open while connecting a monitor or switching modes between Duplicate, Second screen only, or PC screen only, the start menu either just gets stuck on the taskbar or does this weird thing where the start menu is behind the taskbar and does not move.
I used to face this almost on a daily basis on my personal laptop (which is on Windows 11) when I connected my external monitor, but not on my work laptop which is still on Windows 10. The only solution to this would be to close the start menu before connecting an external monitor or changing modes. I have not looked through Windows 11 known issues so do not know if this is a bug that is known or reported. I should probably look in the feedback hub and report this is not already.
Hope this helps.
Edit: in case the start menu is already stuck, open Task Manager (Ctrl + Shift + Esc) and restart the Windows Explorer.