I previously said that I was experiencing the same issue. I went to Genius Bar and they told me to wait for future updates since my battery draining might be caused by some compatibility issues. Today, I accidentally noticed that a process from "Karabiner-Elements.app" is occupying a great amount of CPU usage (this is an app used to customize keyboard functions). So I tried to uninstall it and it worked. Now my Mac has returned to normal (see pic attached). It turned out that my "Karabiner-Elements.app" was not updated to the latest version to work seamlessly with macOS Big Sur.
So my suggestion here would be to:
First, check App Store for app updates;
Second, check the official website of third-party apps you downloaded from web to see whether they have updated their apps for macOS Big Sur. If not, you can try uninstall them to see whether it will help (if the app is not a must-have for you).
Lastly, if software side is okay, try running system's hardware check to see if there is something problematic.
Hope this can be of some help to you!!