Apparently this is obvious for anyone else, since I didn't find this question posted elsewhere. So, what happens?

Obviously, you reshuffle the card and all the discarded Mythos cards into a new deck and draw again. But what about active Environments? What about active Rumors? Are those reshuffled as well?

You reshuffle the deck. Active rumors and environments, and even headlines that say "leave this card in play to indicate X effect," are not in the deck.