Welcome, david_0908, to Apple Support Communities!
After you did a «clean re-install», did you test to see if you still had the problem, before restoring your files? And before restoring your old software?
Clean Installs of Big Sur have been a “sure fire” “fix”, because there is no problem with only Big Sur. (With the exception of potential hardware issues, with some older systems.)
After restoring files, but before restoring old software, there is a “housekeeping” period as Big Sur—much like previous major Operating System (OS) upgrades—analyze, reindex, and cache files, photos, music, videos, books, etc., in preparation for your daily use and convenience.
Depending upon how much stuff was “suddenly” put on Big Sur’s “plate”, so to speak, and how fast your system is (including how fast your drive is), this “housekeeping” should “settle down”, once it “catches up” with your files, in a day or so of continuous work.
People not using battery capable systems (read MacBooks) usually don’t notice this much at all, unless, like me, they run always with the Activity Monitor running.
Running on batteries, on the other hand, makes this “housekeeping” period far more apparent, and, if the user is not aware of what is going on, hugely worrying!
Finally, once your old software is restored, you introduce a huge new “dimension” of potential issues that can result from third-party software that can be “confused” by the major OS upgrade—a potentially huge change in the system upon which they are running: they may simply not run, or they may “run amuck”.
If the third-party software goes “amuck”, it is possible that no amount of waiting will permit the system to “settle down”!
All one can do is search out the errant software, and take appropriate action: termination, removal, upgrade, etc.
I have been, quite frankly, surprised that we haven’t seen more issues with third-party software, with this major OS upgrade!
Such is usually far more common than we have been seeing, but it has certainly been happening.
Unless you have a hardware issue—we all hope you don’t!—high Energy use can only occur due to high computer resource use (like CPU, GPU, RAM, disk, networking, etc.) by programs!
The typical culprits will not be the applications you, as the user, have chosen to run and interact with, since, if those “misbehave”, you, typically, notice right off.
So, the usual culprits will be background processes that you usually do not see, unless you more specifically look for them!
This is where Activity Monitor (Launchpad -> Other -> Activity Monitor) comes in!
Note that with the default Views, you will only see “My Processes”.
Change the Views to “All Processes” (I usually run with “All Processes, Hierarchically”, so I can see the relationship between processes and their subprocesses), in order to see what is actually going on, “under the hood”, on your computer.
Note: Unfortunately, it appears that not all background processes have been “instrumented” for Energy use. So the processes and their Energy use, as seen in the Energy tab, of Activity Monitor, is, likely, incomplete. However, fortunately, the overall Energy Impact doesn’t require all processes to be so “instrumented”.
Take a good look around. Reorder the views to show the highest CPU, GPU, etc. “users”.
You may be quite surprised to see what is working your computer so hard!
Now, you can be better equipped to take appropriate action, on your own computer!