I've been using SSH for ~15 years and never knew about these escape sequences. I'm eagerly awaiting my next hung session so that I can test `~.`. It's much nicer than my current approach of having to close that terminal window.
My other favourite is I very often SSH with -v to figure out why the connection is hanging, you rapidly figure out if DNS is failing, the TCP connection doesn't open, it does open but no traffic flows at all or it opens and SSH negotiation starts but never finishes. You can learn a lot just from this about what is wrong.