I personally try to only update an app from the app stores I downloaded them from. I’ve never experienced an issue from a cross app store update, and don’t think there would be. Me only updating from the app store from where I downloaded it is all my personal preference and not based in any research I’ve done.
I imagine some of the connections are “legitimately” needed to access Play apps, but why go that route if you can get F-Droid apps cleanly? I haven’t tested acquiring F-Droid apps from App Lounge, so maybe there’s less background activity in that situation…I don’t know.