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.
If hung SSH connections are common it's likely due to CGNAT which use aggressively low TCP timeouts. e.g. I've found all UK mobile carriers set their TCP timeout as low as 5 minutes. The "default" is supposed to be 2 hours, you could literally sleep your computer, zero packets, and an SSH connection would continue to work an hour later, and generally speaking this is still true unless CGNAT is in the way. If you are…
Depends on whether your sockets survive that, though. Especially on Wi-Fi, many implementations will reset your interface when sleeping, and sockets usually don't survive that.
Even if they do, if the remote side has heartbeats/keepalive enabled (at the TCP or SSH level), your connection might be torn down from the server side.