It is technically possible that the person(s) operating a room server might access or track the following information from each client:
SSB ID IP address
The room server cannot know anything else about your account, none of your feed messages, none of your profile pictures. We advise to only connect to rooms operated by trusted people if you're not comfortable sharing the 2 pieces of information listed above with strangers. Granted, SSB rooms leak significantly less personal information than SSB pubs do.
In the rare situation that the source code for the room server was modified, then it is possible that the room server acts like a pub server, and as such it could fetch your public feed data, profile picture, etc.