I haven’t seen such a recommendation in the official support guide or anywhere, but if you know of one, could you share it with us? I prefer to use software in accordance with the official documentation.
Anonymity isn’t a feature promised by this browser or Mullvad VPN anyway.
There’s no benefit to using it, but is there any downside? I don’t think so. Perhaps websites might consider the ESR versions (which come pre-installed by default in distributions like Leap and Debian) to be outdated and prefer to enable their content on any browser that offers more modern features. A while back, the Element web app didn’t support Firefox ESR.
Tor traffic is already being detected and blocked, but I can say that, aside from the restrictions I’ve experienced due to VPN usage with the Mullvad Browser, I haven’t encountered any blocking issues.