feat(lobby): enter the game immediately and wait for the opponent inside it

Quick auto-match no longer waits on a separate screen: Enqueue opens a real game seating the caller with an empty opponent seat (new game status 'open') and the player enters it at once. A second human searching the same variant+rule joins that open game; otherwise a background reaper seats a robot after a 90s + random 0-90s wait, pushing a new in-app opponent_joined event that fills the opponent card and re-enables resign and chat in place.

Matchmaking state is now the open games in the database (the in-memory pool, lobby.poll and lobby.cancel are gone), serialised by a per-bucket advisory lock. While a game is open the starter may move on their turn, but resign, chat and nudge are refused; the lobby and opponent card show "searching for opponent".

Schema edited in the baseline (no prod data): 'open' status, nullable game_players.account_id for the empty seat, and a games.open_deadline_at stamp; jet code regenerated.

backend/internal/lobby/lobby.go

@@ -1,9 +1,10 @@
-// Package lobby forms games: an in-memory matchmaking pool that pairs two humans
-// for an auto-match, and friend-game invitations (invite -> accept) that start a
-// 2-4 player game once every invitee has accepted. Both produce a game through the
-// game domain (a GameCreator); neither imports the engine. The matchmaking pool
-// is in-memory and lost on restart (players re-queue); the robot that substitutes
-// for a missing human after a short wait is added in a later stage.
+// Package lobby forms games: an auto-match maker that drops a player straight into a
+// game with an empty opponent seat (or joins them into another player's waiting one),
+// and friend-game invitations (invite -> accept) that start a 2-4 player game once
+// every invitee has accepted. Both produce games through the game domain; neither
+// imports the engine. Auto-match state is the open games in the database, so it
+// survives a restart; a background reaper substitutes a pooled robot for any open game
+// that waits too long, guaranteeing every game gets an opponent.
 package lobby
 
 import (
@@ -22,8 +23,8 @@ import (
 type GameCreator interface {
 	Create(ctx context.Context, params game.CreateParams) (game.Game, error)
 	// InitialState returns a seated player's full initial view of a started game, used
-	// to enrich the match_found / game_started events so the client renders the new game
-	// without a follow-up fetch.
+	// to enrich the game_started event so the client renders the new game without a
+	// follow-up fetch.
 	InitialState(ctx context.Context, gameID, accountID uuid.UUID) (notify.PlayerState, error)
 }
 
@@ -51,8 +52,6 @@ const (
 
 // Sentinel errors returned by the lobby.
 var (
-	// ErrAlreadyQueued is returned when an account already waits in a pool.
-	ErrAlreadyQueued = errors.New("lobby: account already in the matchmaking pool")
 	// ErrInvalidInvitation is returned for a malformed invitation (bad player
 	// count, duplicate or self invitee, or unacceptable settings).
 	ErrInvalidInvitation = errors.New("lobby: invalid invitation")