I'm also having issues with my MacBook Pro 15" (late-2013) stalling at shutdown/restart/force shutdown. If I do a standard shutdown/restart, it'll log out of my user account perfectly fine and the screen would go black (as it's been powered off). However, I know that it hasn't powered off yet for maybe 30-60 seconds or so?
I know it's still on, because if I try to power on my MacBook it won't register my keyboard 'power on' press because it's still trying to power off/shutdown. Similarly if I let it reboot itself it takes around 30-60 seconds between logging out/screen appearing off and then having the Apple Logo/Sound boot up. Even force reboot has the same issue, always 30-60 seconds from the moment the screen goes off until when the Apple Logo/Sound boot up.
Going through Console log, I can't see any power/shutdown logs with any information, so does anyone know what other logs I should look at, or is there a reverse Verbose mode for shutdowns (like when it boots up but for shutdown instead)?
I've also read something that this shutdown/reboot stall might be because of non-APFS disks (both internal or external disks plugged in at the time of shutdown). However, the only non-APFS disk I have is my Windows Bootcamp (NTFS) partition on my MacBook, so I wonder if this is somehow stalling it? If this is the culprit, can I reformat it to APFS (or is this only available on macOS)? If someone with more technical experience around the disk/file system structures could see if this fixes/replicates the issue, that would be highly appreciated!
Otherwise, I've found the operating system far FAR more stable than previous systems from the initial release, other than a small lag when clicking in MATLAB and lag when typing in Microsoft Outlook (rarely). Remember also, I am typing this from the oldest supported MacBook Pro for Big Sur, which is performing far smoother than my previous operating system (Mojave).
So from a stability-standpoint, your experience of Big Sur is very much isolated to you and your device, and isn't affecting every user running Big Sur.