Private browsing is equivalent to creating an ephemeral browser profile everytime. It might get rid of more browser storage, but for how tracking works now-a-days, it is useless. It is only for what you want to store on your disk, not for how you want to be seen to remotes.
I assume a subset of these bits could be used, meaning the "unique" or not claim of this test probably doesn't reflect if you can be tracked. I also assume that a VPN would help tremendously.
For that test, as is, I get "unique" every refresh when using Brave Browser. With Safari and Chrome, I get a fail an subsequent sessions.