Hey there!
I’ve been there, good suggestions so far, I typically check the usual suspects, login items, apps/processes running in the background that may just not like Big Sur (At least not yet).
I have had luck with removing old software kext Extensions, if I have a backup and find any I don’t need it use, I typically delete them, (Sometimes uninstallers don’t affect these locations, especially with the security now, and running older programs, etc).
Although doing a clean install will probably fix it, I may also head over to:
Apple logo > About This Mac > System Report.
Under the software section, click “Extensions”. They may take a while to load.
Once they have loaded, click once on “Obtained From” on the top right tab, to sort out the Apple extensions from the others. (You May have to expand the window to see it, or go to full screen).
Then, if you scroll to the bottom, under “Obtained From”, you’ll see all third party kexts. If I have a backup I definitely delete any that say “Unsigned” and sometimes even some from “Identified Developers” if I don’t need or use the program associated with it.
Once you click on one, it’ll show the file path/location below, typically:
Finder/Go/Macintosh/Library/Extensions, or even in /Frameworks, as I’ve seen with some VPN’s
They used to also use:
Finder/Go/Macintosh/System/Library, but I believe with the security now they can’t.
Anyhow, deleting those, and removing all login items from System Preferences > Users and Groups, and restarting may be a good step.
Of course safe boot may tell you more about the cause, as testing in a new user, but I’ve often found files in these locations to be the cause.
Another revealing test may also be disabling the internet all together, and test, to see if it’s caused by an app or process hogging your network or not, (Although I’d think of that were the case, you’d see in the network tab of Activity Monitor, some process, Apple or not rising).
If the battery draining is so bad, but was fine with Catalina, and you DO do a clean install/reset, probably not migrating all the data, (Which includes all hidden and system files) would be a good idea but manually backing up/moving data back on. Or, as always you could restore your Time Machine backup if you have one, until the problem is sorted out, or found in the first place.
Apple maybe able to help with a more direct solution, if you’re willing to give a call and provide the logs necessary if all else fails, it is a new system, so I’m sure there is other software/hardware that maybe conflicting with it, and this would be good for them to know.
Whatever the case, hope all goes smoothly!
Activity Monitor user guide:
https://support.apple.com/guide/activity-monitor/welcome/mac
How you can also use Terminal, this maybe useful as well:
https://www.google.com/amp/s/www.chriswrites.com/how-to-view-and-kill-processes-using-the-terminal-in-mac-os-x/amp/
If you are in contact with Apple Support though, I’d stick with their direction, best of luck!