I get a lot of these and try to assume that it's the person wanting to be polite. Starting a conversation without a greeting is very rude in a lot of cultures. But yes, it's annoying in chat form, and especially when the conversation is left dangling. Depending on the situation, I'll write out what I'd like to say, then copy it before starting off with a "hello". If the person starts typing, I'm ready to follow up with the request. If not, I'll prepend it with: "when you have a minute", or whatever makes sense given the urgency of the request. And I'll generally only start with the "hello" if it's the first time we've interacted that day.

We've also experimented a little bit on my team with prepending asynchronous messages with emojis: a turtle means you can take your time, an alarm means it's urgent, a custom thumbs up/thumbs down emoji means you just need a yes or no answer.