As an example:

Mass effect Andromeda has a co-op tag, even if 99,9% of the game is purely single player. It has a side thing that is completely optional that you can play co-op where you fight hoards of enemies but nobody buys the game for that.

So the suggesion is to break it up into two separate co-op tags:

Co-op: The main content of the game is co-op, meaning in the mass effect game it would mean that you can play the main campaign co-op with friends.

Co-op elements: Some part of the game is co-op, but not the main content of the game.

That way if you sorted for co-op games to play with friends, you don't have to do research on every single game with a co-op tag just to realise that it is limited or only a specific game mode, or limits you to only a small part of a game or anything like that.