It has nothing to do with anxiety for me, personally, and everything to do with simple courtesy. When my colleagues message me things like this, this is the conversation we have:

Colleague: "Hey, do you have a minute to get on a call?"

Me: "Maybe. What is it about?"

Colleague: "I was looking at X and had a question."

Me: "I can meet with ..."

Why not cut the chase here and start with "I was looking at X and had a question, do you have a minute?"

I almost never do have a minute without notice but I'm happy to find a few minutes to give people. I don't like having to play this 21-questions game with people to find out what they need, though. It really irks me.

It really depends on the person.

Some people you can say you have a question and it'll occupy their mind not knowing what it is.

Some people can happily just wait until the actual question comes through, but once it does that's the thing they're thinking of.

"Do you have a minute" and "Do you have a minute, I've an issue with X" have problems, but for different people.

I can expand on this more later but neither myself nor the OP have put it as some general rule. I don't see any implication that it should be done everywhere to everyone.

I benefit from quick realtime comms too, and understand people are different (that's the main thrust of my comment). I don't know if others realise just how unproductive it can be for some of these styles of messages though.