This would primarily affect web servers exposing SSH access to the public right? I suppose it also affects internally accessible servers as well but to a lesser degree in terms of priority.
Both SSH and SSL base on TLS. The leak in question has a problem
> during or after a TLS 1.3 handshake
Sure, openSSL is not SSH, but it is not unreasonable to assume this leak may affect web servers as well (e.g. by being based on the same underlying TLS implementation).
"SSH != SSL" is a bit short to invalidate the assumption of the OP. I'd not be so sure this problem does not affect "web server X".