I think the auction and bidding key words can be merged (and I would suggest auction as the key word as bidding and bedding are almost homophones in some dialects).
There is something to be said for the collection. As a small twist, though, not all of the "bidding" games are auction games. People have also used "bidding" as a tag for trick-taking games in which players bid a number of tricks.
Ah, correct indeed. Bidding is also the phase in many card games to determine the trump suit (though this is also sometimes referred to as "auction"). The bidding in Hearts, by contrast, is rather a sort of betting in that it tries to predict the future for fun and profit, or loss, but bidding stuck as a term. So yeah, can't really get rid of the term.
You're right, though, that it doesn't make sense to have one tag for both bidding in an auction and bidding for tricks. So I've removed "bidding" from the auction games and changed it to "trick-bidding" for the trick-taking games. Not perfect, but better maybe.