After restating the problem, I still don't know where you are trying to create a folder.
I can only guess it is within the home folder since you talked about the permissions, but I'm still not sure.
There are lots of places you can't modify, but you should be able to create a folder anywhere in your home folder.
I also don't know exactly what the Sharing & Permissions section fully states. It appears your user account has read/write to the home folder and the "others," whatever those may be.
What about the group and what permissions does it have.
How about everyone?
What does it state at the top of the list? Does it state you can read and write, or does it state that you have custom access.
I am hoping Apple will see this post and forward the issue to Big Sur engineering.
Apple doesn't monitor this forum for those types of things.
I'm not sure what Big Sur engineering would be able to do. We haven't managed to figure out why you are seeing the problem.