"Just because the chat app shows that you are logged in, it does not mean that you are immediately available to chat."
It's 2022, chat app statuses are more sophisticated than just "online/offline" indicators. It will tell you if I'm busy, if I'm in a call, if I'm presenting, if I've been AFK, etc. If I'm online and none of those statuses are true, I can probably engage now.
"If I want to leave a message for someone with a response accepted at their convenience, then I send an email. If I reach out via chat, it's because I expect a realtime exchange. Again, because the little green dot appears next to user's name does not mean they are not deep in the tall grass and readily available to chat."
Saying "hello" before asking a question doesn't somehow increase the chances that I will be more available. You can ask what you need in the first message, and if I can't respond despite my chat status, I will get to it when I can, at which point we can have the realtime discussion. You don't get a realtime exchange by saying "hello" and then waiting for an answer.
"To me, chat is just like walking up to someone at the cubicle to have a conversation."
Except it's not. There is a distinct difference in the mode of communication here. You wouldn't walk up to someone's desk, hand them a letter, and then leave, but that's exactly what you can do with a chat. While chat is more real-time than email, it is still a written record and it's slower than an actual conversation; as a result, it comes with its own set of pros and cons that facilitate things differently.
"If I walk up to someone and notice they are deep in it, I don't bother them. Chat doesn't allow for that kind of signaling, so a "got a sec?" isn't a wast of time as it allows for them to not reply indicating "no" without stopping to type "no"."
Again, it does signal that, with status icons. And even if my status is green but I happen to still be busy for some reason, a chat notification is a chat notification. Saying "hello" is as much an intrusion as saying "hello, I have this problem with <x>, can you help me?" -- except if you just say "hello", then I have to respond and then wait more time for a second intrusive notification to find out what you need.