A general rule is to NOT upgrade while an issue exists
in the system presently in your Mac. This only clouds
a chance to resolve an issue, within its natural setting.
And some older Macs generally are marginal at best
where a newer cutting-edge macOS is concerned.
The best advice (short of reinstalling an even older
macOS Catalina -- requires backups and new install)
..Is to attempt to resolve Big Sur by using full new
install of Big Sur; as the 'newest updates' may fix it.
Each step within the system build may not have worked
so if there's an issue in Big Sur, resolve it from there.
Good luck & happy trails! ☺︎