Well, you could go to brave://flags and start disabling Brave features to find one that is causing issues, you can start with the ones you might not use, like Wallet and Web3 and rewards.
Brave features are on top of the list, from the first one to the one that talks about Temporarily unexpire M112 flags.
So you can easily disable them, and test.
Did you try to go to the same website in Private mode? it could be anything if it is the Brave Process.
If you disable hardware acceleration, enable it as well, the browser will consume more CPU if you disabled the HW, that’s why it is there for, to use the GPU cores which are way more than the CPU ones, just make sure you have your drivers updated so it works properly, or better, since Browsers HWacc is not the greatest thing either.
CPU should only be higher when loading websites, or a really heavy website.
I mean you could try some troubleshooting techniques like to start brave with brave.exe --user-data-dir=c:\whatevertemporarypath and test to see if a new profile affects the CPU or maybe some update caused this issue, that good thing about doing it that way is that you won’t touch your normal User Data, and you can open both at the same time to test and compare both versions.