I installed the latest Windows 11 update (KB5013943), and upon reboot I have a similar issue except my taskbar is completely blank. Start11 still opens up if I hit the Windows key and I can Alt-Tab windows.
When I open up Start11 settings and go to 'Taskbar', in red at the top says "You already have something else managing your taskbar buttons so this cannot be enabled until that is disabled." This is on 1.2. I have not adjusted anything other than the Windows 11 update.
Update: I installed 1.22 and rebooted and everything is back to normal.