All host info not accessible via X11 protocol is hidden, for example font list, is replaced with generic one.

For even more protection, run VNC server with common resolution in the container and connect to it using VNC viewer. In this case firefox provides a super generic profile (latest debian with mesa GPU), making this browser very hard to distinguish from others. This has some downsides however: First, you cannot resize window. Second, a lot of actual bots use same config, so it might be blocked.

mullvad browser is pretty much this, but without messing around with containers. One fingerprint for all users, with the same font list, resolution, canvas behavior, etc.

https://mullvad.net/browser

looking at https://mullvad.net/en/browser/hard-facts , Mullvad browser is much more extreme: many APIs blocked, always incognito mode... I would not be surprised if this blocks some sites.

the container approach on the other hand is bog-standard firefox.

Isn't it suspicious bot-like behavior to only have the bare minimum fonts installed? :-)

To be fair, Firefox out of the box prevents against font fingerprinting more than Chrome, it's considerably easier to get Firefox to run in a docker container and pass all the client side challenges than Chrome in my experience, you still have a valid point though.

OP mentioned that they run a heavily modified browser, I think it means compiled with changes - docker means stock Firefox