Mythic Masters walk together: an empty room forgets the region's wilds, and the mythic hunt isn't kept (leftovers of #3859)

Part of #3859 (leaves it open). #3875 keeps the region's wilds for a late joiner while someone is in the room. Left: (1) when the room empties it forgets the wilds, so the next visitor gets a fresh roll; (2) the mythic/hunt state isn't kept for a late joiner. Smallest slice: persist both in the room's storage, one journey test through the running app (join, leave, rejoin).