You don’t need to search any farther than the Apple Support Communities, pvmikev1, to find quite similar “complaints” and “issues” about previous upgrades (not just updates).
Just because you, personally, haven’t experienced such, doesn’t mean they didn’t happen.
(I’ve never experienced such, myself, but, fortunately, I, like many others, understand what is going on.)
Since the problem occurs with «software that [y’all were] running under [a previous version of macOS, such as] Catalina», your protestation that «[you] don't have any software that [you weren’t] running under Catalina» is more of an indictment than anything close to an absolution.
Here’s the sure-fire solution:
- Backup everything you want to keep! A full backup!
- A truly clean install of Big Sur: absolutely nothing carried over from your previous Operating System (OS). You will find that your system “settles down” almost immediately! You’ll see that you have at least as good battery life (time to discharge) as you ever did. (Really, if not, then your battery has a problem, or, possibly, you may have other hardware issues: we hope not, but this is a possibility which is included within the “old timers” experience.)
- Then, once you have found your system to be good with the new OS, you migrate over your data—only your data—absolutely no software! Yet! This will start the various “housekeeping” background processes! Your Energy usage will go back up, while these processes prepare your system and data for your everyday use. Depending upon how much data you “suddenly” “dumped” upon the OS’ “plate”, so to speak, this may take a few days to “settle down”.
- There may be issues with certain settings, which may require synchronization with data on iCloud and on other devices (such as synchronization between Safari on multiple devices, for instance). Even this should “settle down”, in time, depending upon how much data and how fast your Internet connection is.
- Once the system has “caught up” with your data; now you can try to restore your programs, Apps, utilities, and other diverse software. This is the most likely place where y’all will find issues, due to old software, that ran “just fine” on the older OS, but are simply not ready for the new OS.
If you run into problems at stage 4, you’ll have to upgrade your software.
Note: Generally, one should always check software compatibility before any major OS upgrade!
After all, not all software even has upgraded versions that are compatible with such a major OS upgrade. (I know many major developers that, while they plan on having compatible versions, have yet to release such new, compatible versions.)