Brave has built in fingerprinting protection (https://github.com/brave/brave-browser/wiki/Fingerprinting-P...), that's enabled by default. It seems like it's less aggressive than firefox's though (since firefox's fingerprint protection is disabled by default because it breaks things), and it doesn't seem to be able to block this companies fingerprinting tech. I got the same ID in a regular window and private browsing window.

The brave shields setting section also has an option for blocking scripts, which may work. It prevents the demo from being able to show an identifier for the user at all, but I'm not sure if it's preventing identification or just preventing the displaying of the identification.