When you look at “stellar nurseries” such as the famous Hubble Eagle Nebula shot, there seems to be quite a bit of turbulence, I guess you could call it, with swirls of various orientations. I don’t think the galactic rotation is imparted to these swirls in the same way the presumed proto-solar system imparted its rotation to the planets. This would be because the galactic scale is so huge, and the stars are imbedded in a thickness much greater than the size of a planetary system.
Just my own musings!