The Star Trek Starfleet Command logo first appeared in DS9 Season 4, "The Rules of Engagement", September 1997.
It was created by Michael Okuda and was "intended to be somewhat reminiscent of the NASA emblem."
The Space Force logo is an iteration of the Air Force Space Command badge which has been around since 1982.
Frankly, I don't see any recognizable constellations in the Northern hemisphere, but will have to rely on the Aussies and Kiwis for Southern hemisphere ideas.
I think they are just random stars.