Q: how do I know which albums a photo is associated with

Photos does not show a ist of albums, but try Jaques Rioux's script. It will work for standard albums, but not smart albums.

See this user tip:  How to find out the albums a photo is in: Jacques Rioux's script

e.g.: "All Photos", "Favourites"

Any photo will be in All Photos, and you can see, if it is in Favorites by looking at the ♡-badge in the Info panel or as a badge overlay on the thumbnail.

And Old Toad has posted that and a few other scripts compiled into applications - http://www.oldtoadstutorials.net/No.P01.html

LN