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/lobby_test.go

@@ -30,31 +30,67 @@ func englishInvite() lobby.InvitationSettings {
 	}
 }
 
-func TestMatchmakingPairsAndStartsGame(t *testing.T) {
+func TestMatchmakingOpensThenJoins(t *testing.T) {
 	ctx := context.Background()
-	mm := newMatchmaker(t, newRobotService(t, newGameService()), 10*time.Second)
+	clearOpenGames(t)
+	mm := newMatchmaker(t, newRobotService(t, newGameService()), 90*time.Second, 90*time.Second)
 	a, b := provisionAccount(t), provisionAccount(t)
 
+	// The first player opens a game and enters it immediately, still awaiting an opponent.
 	r1, err := mm.Enqueue(ctx, a, engine.VariantEnglish, true)
 	if err != nil {
 		t.Fatalf("enqueue a: %v", err)
 	}
 	if r1.Matched {
-		t.Fatal("first enqueue must wait")
+		t.Fatal("first enqueue must open a game awaiting an opponent, not match")
 	}
+	if _, _, status, err := newGameService().Participants(ctx, r1.Game.ID); err != nil || status != "open" {
+		t.Fatalf("opened game status = %q err %v, want open", status, err)
+	}
+
+	// A second player for the same variant and rule joins that open game, which starts.
 	r2, err := mm.Enqueue(ctx, b, engine.VariantEnglish, true)
 	if err != nil {
 		t.Fatalf("enqueue b: %v", err)
 	}
-	if !r2.Matched {
-		t.Fatal("second enqueue must match")
+	if !r2.Matched || r2.Game.ID != r1.Game.ID {
+		t.Fatalf("second enqueue = (matched %v, game %s), want it to join the open game %s", r2.Matched, r2.Game.ID, r1.Game.ID)
 	}
 	seats, _, status, err := newGameService().Participants(ctx, r2.Game.ID)
 	if err != nil {
 		t.Fatalf("participants: %v", err)
 	}
-	if status != "active" || len(seats) != 2 {
-		t.Fatalf("matched game state: status %q seats %v", status, seats)
+	has := func(id uuid.UUID) bool {
+		for _, s := range seats {
+			if s == id {
+				return true
+			}
+		}
+		return false
+	}
+	if status != "active" || len(seats) != 2 || !has(a) || !has(b) {
+		t.Fatalf("joined game: status %q seats %v (want active with a=%s and b=%s)", status, seats, a, b)
+	}
+}
+
+// TestMatchmakingReEnqueueReturnsOwnOpenGame checks a re-enqueue is idempotent: the
+// caller gets their existing open game rather than a second one.
+func TestMatchmakingReEnqueueReturnsOwnOpenGame(t *testing.T) {
+	ctx := context.Background()
+	clearOpenGames(t)
+	mm := newMatchmaker(t, newRobotService(t, newGameService()), 90*time.Second, 90*time.Second)
+	a := provisionAccount(t)
+
+	r1, err := mm.Enqueue(ctx, a, engine.VariantEnglish, true)
+	if err != nil {
+		t.Fatalf("enqueue: %v", err)
+	}
+	r2, err := mm.Enqueue(ctx, a, engine.VariantEnglish, true)
+	if err != nil {
+		t.Fatalf("re-enqueue: %v", err)
+	}
+	if r2.Game.ID != r1.Game.ID || r2.Matched {
+		t.Fatalf("re-enqueue = (game %s, matched %v), want the same open game %s unmatched", r2.Game.ID, r2.Matched, r1.Game.ID)
 	}
 }