netcat, socat and openssl s_client are all available for general manual connection testing.

As are many other tools. But the ones above are basically far better direct telnet alternatives.

I've never really understood why it's a thing to use a telnet client for transmitting text on a socket for purposes other than telnet. My understanding is that telnet is a proper protocol with escape sequences/etc, and even that HTTP/SMTP/etc require things like \r\n for line breaks. Are these protocols just... close enough that it's not a problem in practice for text data?

Because it's there.

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If it's alright to be pedantic, anyone with programming knowledge can do the same without these tools. What these offer is tried and tested secure code for client side needs, clear options and you don't need to hand roll code for.