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/inttest/helpers.go

@@ -56,11 +56,21 @@ func newRobotService(t *testing.T, games *game.Service) *robot.Service {
 	return robot.NewService(games, account.NewStore(testDB), newSocialService(), noop.NewMeterProvider().Meter("robot-test"), zap.NewNop())
 }
 
-// newMatchmaker builds a matchmaker starting real games and substituting from
-// robots after wait.
-func newMatchmaker(t *testing.T, robots lobby.RobotProvider, wait time.Duration) *lobby.Matchmaker {
+// newMatchmaker builds a matchmaker opening real games and substituting from robots
+// after minWait plus a random jitter in [0, jitter).
+func newMatchmaker(t *testing.T, robots lobby.RobotProvider, minWait, jitter time.Duration) *lobby.Matchmaker {
 	t.Helper()
-	return lobby.NewMatchmaker(newGameService(), robots, wait, zap.NewNop())
+	return lobby.NewMatchmaker(newGameService(), robots, minWait, jitter, zap.NewNop())
+}
+
+// clearOpenGames deletes every open (awaiting-opponent) game so a matchmaking test
+// starts from a clean slate: the shared test database is FIFO-joined across tests, so a
+// leftover open game would otherwise be joined (or opened-into) instead of a fresh one.
+func clearOpenGames(t *testing.T) {
+	t.Helper()
+	if _, err := testDB.ExecContext(context.Background(), `DELETE FROM backend.games WHERE status = 'open'`); err != nil {
+		t.Fatalf("clear open games: %v", err)
+	}
 }
 
 // provisionAccount creates a fresh durable account and returns its id.