Redo the SMC and NVRAM resets like 3 or 4 times in a row each and then restart holding Shift to load macOS in Safe Mode
Check if the problem happens there too.
If yes, I advise you to try a clean install of Big Sur.
If you decide to go for a clean install, here's a quick guide:
First, backup to an external drive (always do that before updating or upgrading macOS versions). In your case I'd say simply copy paste your personal data because the is going to be reinstalled from zero.
Create a bootable installer How to create a bootable installer for macOS - Apple Support
Restart holding Option and choose the installer. It'll load Recovery Mode.
Once loaded, open Disk Utility and completely wipe the disk, erase everything, all volumes and partition.
Close DU and start installation.
Once done, setup your Mac as new, allow it to update everything it asks for and check the battery condition.
Reinstall you apps and copy back your data.
If that doesn't work, you better call Apple Support and then take your Mac to an Apple Store or Authorized for a proper check.