If you want to be properly anonymous, don't use public key authentication (ssh -o 'PubkeyAuthentication no' username@ssh.chat). Otherwise, anyone in the chat can /whois you and get your public key hash - and they could pretty easily deanonymize you if you use that same key on GitHub (<a href="https://blog.benjojo.co.uk/post/auditing-github-users-keys" rel="nofollow">https://blog.benjojo.co.uk/post/auditing-github-users-keys</a>) or potentially other services.
A professor of mine offered small extra credit over zoom classes if we found ways to cheat. We took our exams on an online IDE that had a built in shell with networking. SSH chat was an easy 5 points.