the only way to check how many copies you have of something is manually scrolling to it in your library when sorted. Searching on the left doesnt show a count, the store page of a game just always says "its in your library" not "its in your library VIA FAM ACCOUNT #2" or something.

Trying to buy a few copies of some co-op games and figuring out who actually has it or how many copies needed is a bit tedious.