Earlier quoted context omitted.
Simply download the Tor browser and evaluate its performance on one of the many browser fingerprint [1][2] and browser leak [3][4] web services. The last time I checked, it didn't pass every test. [1] https://www.amiunique.org/fp [2] https://coveryourtracks.eff.org/ [3] https://browserleaks.com/ [4] https://www.dnsleaktest.com/
Indeed, my fingerprint in https://www.amiunique.org/fp appears to be unique when using the Mullvad browser.
It mixes a lot - fonts returned, media devices, the canvas ID - it's pretty good and similar to what you expect from the improvements out of Tor Browser
[0] using amiunique and fingerprint.js (now fingerprint.com) - which most of the nefarious ad networks use
[1] not that just as with Tor, you have to quit the browser or click the 'new identity' menu button. just closing a tab/window and re-opening is not enough. I've always believed that there could be a UI hint to this in private browsers with a unique color/background in the menubar as an indicator