You don't do a HTTPS handshake by hand. That's what openssl s_client is for.
https://docs.openssl.org/1.0.2/man1/s_client/
Or maybe socat, I don't use it but I'm pretty sure I've seen people use it.
https://docs.openssl.org/1.0.2/man1/s_client/
Or maybe socat, I don't use it but I'm pretty sure I've seen people use it.
I can't remember the last time I used telnet to test whether a web server was live. I don't think web servers figure very prominently in the work I do, though not zero, for sure. However, I doubt I'm the only one in that boat.
The concept of protocols made up of printable characters delimited by new lines is antiquated.
All of those problems have different root causes and therefore have different solutions. Telnet helps you figure out where in the stack the failure is occurring.