These seem to be based on some core concepts of psychology and interpersonal influence (intended or not). I used to work in that area and picked up a few of these tricks along the way too.

Basically what they do is give your recipient a clear call to action-if you want them to do something, it’s best to ask directly VS tiptoeing around. The best example there being the just wanted to check in one. If you want an update, ask for it. That way there’s no ambiguity what the response needs to be and they can fire it off quickly without thinking. You can wordsmith it to fit your style and company culture but the point is to tell them what you want them to do.

The other thing I see here is a sort of 2-parter. It’s about conveying confidence and positivity in your tone. There’s a lot of nuance to this and personal communication style and context of the situation play in more. But basically these items like ‘nice catch!’ and ‘thanks for your patience’ all kind of do this, showing a kind of team player attitude that also demonstrates that you know your own worth. ‘Happy to help’ does something similar but is more subtle-it avoids the negative tone of things like ‘no problem’ and goes a bit further.

Individually theses communications may have a minimal impact (depending on the situation of course) but over time using this kind of language associates you with positivity and confidence and can help you with with you building work relationships.