Well, you can just add a simple message to be more specific about what you are talking about and it would not cause someone fear that they screwed up something.

I think it actually adds some of the human part back in. "Hey, got a sec?" in person comes with quite a bit more context--body language, tone of voice--and a pretty quick transition into the content.

To me, the rhythm of an informative first message feels more natural than responding to someone's ping and waiting 2 minutes for the follow-up.