Joe, thanks good info. Well first thing? On laptop, Photos, I don't see word Library in the software Photos anywhere, maybe I missed it. (you were not talking about finder, Library correct?); you are saying within opened software Photos -- Library. I don't see it in menu or sidebar...

But I do see on laptop, Photos software on left ALBUMS, recently deleted, and in fact there are a lot of deleted images there. And a lot of those recently deleted are are the ones polluting the desktop version of photos.

Strangely on the desktop, Photos, there is no recently deleted on the left sidebar.

You tell me what you make of this, all over my head, and if you think I should just bring over the finder library to the desktop. And also should / can you permanently delete from the recently deleted? (ie empty trash) good idea?

Once the two are blessed/ harmonious in sync, I'll have follow up question at that point on your nice settings screenshot..., and your method of bribing photos into the system....