You’re not making any sense. Brave is supposed to counter fingerprinting even without a VPN, and without cleaning. That’s why they refer to using the browser normally on Cover Your Tracks.
The problem is that they face other tech that they can’t counter, so they dismiss it as “biased” and something meant to make money. WTF.
Don’t use a cleaning session and a different exit. Use it normally, just like most users. And then do the same for Brave and Librewolf.
Even better, try the two addons which I mentioned, and which you claim don’t work, and see how the site performs.
Finally, I’m sure that there are browsers that can work against it, and one of them is Pola, but those are paid browsers.