The Coven contested

You're conflating goes in play with resolved. When The Coven resolves, you gain a trifle MPA (if possible) and it would go in play, but because it contests it does not go into play.

That second point is easier to talk about with regard to Elder Library. If you contest Elder Library, you don't gain then lose a hand size, nothing happens to your hand, as the card never goes into play.