hayrettin193 and @All:
This is not a problem with Big Sur.
This is not a problem Apple can fix, except to better educate users about what to expect from a major Operating System (OS) upgrade, such as this major upgrade from Catalina to Big Sur: an upgrade so major that Apple actually increased the major version number, from 10 to 11, for the first time since 2001!
This OS needs to spend some time reindexing your system, your libraries (such as your photo library), and much else, for your user experience within this new OS. I’ll refer to such as “housekeeping” tasks or work.
The more “stuff” you have on your system, the more work the system will need to do to be fully ready for your use!
Unless you have a hardware issue—such as a short-circuit (potentially even within your battery: a most serious situation!)—the only way a computer will use more power is if it is running more CPU computations, and/or more memory/drive work.
Perhaps now is a good time to become familiar with the Activity Monitor (Launchpad -> Other -> Activity Monitor)!
Don’t just look at the default View of My Processes, but look at All Processes (I set this for Hierarchically, so I can see what processes subprocesses are associated with).
The Energy tab, in Activity Monitor is a good view, but not all processes—especially not all Background processes—seem to be “instrumented” for Energy Use.
Additionally, look at the CPU tab, since the more CPU a process uses, the more energy it uses. (Similarly, the more memory operations and storage operations use more energy. Unfortunately, Activity Monitor doesn’t give us the rates of such use, so this is difficult to ascertain. However, such energy use is usually rather ignorable, compared to CPU and GPU use.)
The normal OS background “housekeeping” tasks will “settle down” after a day or two of continuous work, depending upon how large your various (photo, Mail, etc.) libraries are, and how many files you have.
However, there is also the potential for various third party processes to go “out of whack”, with a major new OS!
Using Activity Monitor, as outlined, above, will help you spot such “errant” tasks, as well.
Some of these third party tasks may “settle down” after some time, while some may never “settle down”!
Many third party programs may need to be upgraded, themselves, to be compatible with this major OS upgrade!