I had only one issue bothering me since install of Security Update 2021-005 that shutdowns needs much longer than before (1-2 minutes! this was way too long compared to before).
So after some googling I decided I should do an SMC and a PRAM reset. Big sur! I mean Big fail!
After doing so my system would not boot anymore.
I tried so far:
1) activating verbose mode -> saw it refused to load some kexts (?)
2) booting in recovery mode and check file system -> no errors found and file system is fine
3) booting in Safe Mode -> It needs endless since it also did a file system check again -> boots fine to GUI otherwise
4) try to reboot in normal (verbose) mode again since, Safe Mode should fix kernel kext cache -> sill hangs because it still refused to load some kexts (?)
5) Boot back into Safe Mode again (still works) and did on terminal a manually try to rebuild kernel cache and fix file permissions in extension folders.
6) try to reboot in normal (verbose) mode again -> sill hangs because it still refused to load some kexts (?)
7) giving up on fixing it since I have a fresh time machine backup and try to reinstall Mojave now...
(and this needs time... I write on my Chromebook now. It just works.

)
I don't know what could be the root cause of this? I installed 2021-005 directly on 2020-001. But even the Apple Software-center itself suggested this as the only available update option (after I reset the previously ignored updates).
I don't installed 2021-005 from within the Software-center since I already had downloaded the 2 GB 2021-005 pkg file of this update. Maybe this caused some problem? But since the pkg was packed into a dmg file that did a CRC check first when opening it I don't thing the pkg was corrupted.
Or that I had such a big jump from 2020-001 to 2021-005? I assume it was at first still using some old cached kexts after install and the PRAM reset trigger a kext cache rebuild and this just revealed the underlying problem that some kexts are not working. But who knows?