Welcome, lukasz292, to Apple Support Communities!
Safari is actually included as a part of the macOS. So, your Safari would have been upgraded with the rest of the system.
An important part of all this, however, is that the typical culprits have not been the software that people interact with, directly, through Graphical User Interfaces (GUIs), but the software that runs in the background, without any GUI.
So, just because you have «no other software running», that you see, does not mean there are not myriad other programs, running in the background, that you cannot see, under ordinary circumstances.
This is why one must use Activity Monitor with the Views set to All Processes, rather than the defaults.
(Unfortunately, it appears that many background processes are not instrumented for Energy Use. So, unfortunately, this means that looking for culprits under the Energy tab, of Activity Monitor, isn’t very helpful.)
Additionally, any system, user, or other software extensions—such as Safari extensions/plug-ins/etc.—are the highly likely culprits.
It has never been the responsibility of an Operating System (OS) or Computer manufacturer to make sure third-party software is compatible.
On the other hand, Apple alerted all major third-party program manufacturers of the upcoming major OS upgrade, well before the expected release: all such manufacturers are always part of the earliest Beta program (potentially even at the Alpha test stage, but I cannot guarantee that), even well before Apple’s World-Wide Developer’s Conference (WWDC), where I learned of the upcoming major OS upgrade, and had the opportunity to join the Developer level Beta test program (well in advance of the Public Beta).
It is up to the individual companies to upgrade/update their software to take advantage of the new OS.
Even at the time of the WWDC, many manufacturers already had new versions well underway. (Some were even demonstrated at WWDC.)
Some admitted they were still working on compatible versions for some of their titles.
Regardless, there is never any expectation that old versions of their software will be compatible with any OS upgrade. (They might be lucky, of course.)
Upgrade vs. update is an important distinction:
- Updated OSs can only ever include compatible OS changes. (So. Your old software should work.)
- Upgraded OSs can, and usually do, include incompatible OS changes. In fact, this is, practically, the only reason for OS upgrades!
Now. I have often characterized Apple’s use of the Update Panel for this major OS upgrade as, what I think of as, a “tactical” error.
Before Big Sur, Apple never provided OS upgrades through the Update Panel, nor the Updates section of the Mac App Store. (That’s why I didn’t even look there, when I was ready to upgrade to Big Sur.)
Instead, one had to search for the new OS, within the Mac App Store (or through retail outlets). (It’s usually not hard to find in the Mac App Store. It’s usually displayed rather prominently.)
While Apple was certainly promoting Big Sur, I think you would find it quite difficult to show that they were indiscriminately «RECOMMEND[ING]» all users to so «upgrade».
After all, the need to check hardware and software compatibility for all OS upgrades (vs. mere updates) has been a standing requirement for as long as we have had electronic computers running Operating Systems (OSs).
As for «an OS downgrade», the offer is to help people in that process, if that’s what they so choose.
I would, absolutely, advise them that such a process is not at all simple, and to always have a good backup, first, just in case.
(Admittedly, one should always have a good backup before an OS upgrade, as well! My first question, for anyone that wants to «downgrade», is “do you have a good backup from before you upgraded?”)