Ubiquitin, the difference is that it’s an adverb, not a preposition. An adverb is a description of an action. In “to stop by”, “stop” is the action, and “by” is the way you are doing it. That’s why you can say “stop by”, without specifying a place; you couldn’t do that with the Yiddish preposition “bei”.
“Stop by” is a synonym of “drop in”. And just as you don’t “drop in your cousin”, but rather you “drop in to your cousin”, or “…at your cousin’s home”, so too with stopping by; you stop by at her home.
I suspect that “stopping by her home”, which you cite from the Cambridge, is either a usage that derives from the Yiddish/German, or else it a modified form of “passing by her home”, but in this case pausing briefly; in that case “by” is being used in the sense of “near”.