Big Sur glitch

Try the SMC Reset and perform this 3 times in a row - then Test.

If no success, try booting into Safe Mode - Shift - Immediately at Startup. Load slowly - normal. It does a Repair disk, clears cache file and loads Only Apple Software and Fonts. Let it run this way for 5 - 7 minutes and shutdown and observe is Issue its or is not there. If Not - would seem to be some Third Party Software interfering with the Normal Shutdown process

Have seen at least two others who had AntiVirus Software installed and it was the cause of weird shutdown issue. Resolution was to Uninstall the Cr$%Ware as per Developers Instructions. If this does apply to your machine - Disregard.

Very interesting - exact same description as your problem by another person - in her case - it was Third Party AV Software playing up. Like yourself, had to Log Out first, then shutdown - all ok but just normal shutdown and disaster.

Yes, hope it does not come back.

What shutdown glitch on what model/year computer?

Please - can you put this is context. What is happening at shutdown?