I remember facing this situation a couple of times and all I did was ignore the initial "Hi", after a long time my interlocutor would insist "Hi? Are you there?"; and then I would finally reply "Yes! I just thought you would continue to write your message and I was waiting".

This "play dumb" strategy worked great for me and I think it has less risk to be perceived as "rude" compared to sending a link to the nohello.com site.

Nice. https://www.nohello.com/ is easier to remember, I'll start doing this.

I think this is often used when the person could save minutes of work if you're around to give some knowledge, but if you're not they'll go ahead and research it. No point in them or you spending more time typing if the connection can't be made in the moment.

I like it. But in the second example they've already finished typing the whole question by the time they said Hi in the first.. then we're told the second way finishes "minutes sooner"? Hmm. That appears to make no sense.

Not wasting the other person's time is however super-important, and a great fast test of whether someone is considerate enough to be an online friend or not.