Sadly the distributions I tried did not open the required port(s) on the built-in firewall (Bazzite and CachyOS, for two).

I would suggest to disable any firewall and check if you can pair.

I found opensuse's default firewall rules were very restrictive and you needed to open a port.

Being Linux, if you were really motivated, you could probably write a shim service that converted CEC to basic input that it does support, or someone out there probably already has.

now, that sounds more interesting than just "unsupported"!