This would be a great use case of SSH over HTTP/3[0]. Sadly it doesn't seem to have gained traction.

[0]: https://www.ietf.org/archive/id/draft-michel-ssh3-00.html

Initial thoughts are it's a meh protocol that does not look well thought-out, has fewer features than SSH, to the point I'm not sure it deserves to be called SSH3 and not telnet-over-websockets. Also, there's already an SSH3 https://marc.info/?l=openssh-unix-dev&m=99840513407690&w=2 so I _really_ think the thing you're thinking of is just some namesquatter assuming it has any connection to openssh or ssh.

I also know how to use SRV records so this is a non-issue for me and everyone I work with.