feat: honest AI opponent in quick game

New Game's quick game gains an explicit opponent selector — 🤖 AI (default)
or 👤 Random player. AI starts a game seated with a pooled robot that joins
and moves at once: no per-move timeout (a 7-day inactivity loss reusing the
turn-timeout sweeper), chat/nudge disabled, no statistics, the opponent shown
as 🤖 everywhere. The random path (disguised robot) is unchanged.

Driven by one game flag (games.vs_ai), set only on AI-started games so the
disguised path is never revealed; Matchmaker.StartVsAI seats the robot
directly (no open pool); the robot replies event-driven via the game service's
after-commit/after-create hook. Wire: vs_ai on EnqueueRequest + GameView.

gateway/internal/backendclient/api.go

@@ -102,6 +102,7 @@ type GameResp struct {
 	ToMove               int        `json:"to_move"`
 	TurnTimeoutSecs      int        `json:"turn_timeout_secs"`
 	MultipleWordsPerTurn bool       `json:"multiple_words_per_turn"`
+	VsAI                 bool       `json:"vs_ai"`
 	MoveCount            int        `json:"move_count"`
 	EndReason            string     `json:"end_reason"`
 	LastActivityUnix     int64      `json:"last_activity_unix"`
@@ -268,12 +269,13 @@ func (c *Client) GameState(ctx context.Context, userID, gameID string, includeAl
 	return out, err
 }
 
-// Enqueue joins the auto-match pool for a variant under a per-turn word rule
-// (multipleWords true is standard Scrabble, false the single-word rule).
-func (c *Client) Enqueue(ctx context.Context, userID, variant string, multipleWords bool) (MatchResp, error) {
+// Enqueue starts a quick game for a variant under a per-turn word rule (multipleWords
+// true is standard Scrabble, false the single-word rule). vsAI true starts an honest-AI
+// game against a robot instead of human auto-match.
+func (c *Client) Enqueue(ctx context.Context, userID, variant string, multipleWords, vsAI bool) (MatchResp, error) {
 	var out MatchResp
 	err := c.do(ctx, http.MethodPost, "/api/v1/user/lobby/enqueue", userID, "",
-		map[string]any{"variant": variant, "multiple_words_per_turn": multipleWords}, &out)
+		map[string]any{"variant": variant, "multiple_words_per_turn": multipleWords, "vs_ai": vsAI}, &out)
 	return out, err
 }
 

gateway/internal/transcode/encode.go

@@ -384,6 +384,7 @@ func toWireGame(g backendclient.GameResp) wire.GameView {
 		ToMove:               g.ToMove,
 		TurnTimeoutSecs:      g.TurnTimeoutSecs,
 		MultipleWordsPerTurn: g.MultipleWordsPerTurn,
+		VsAI:                 g.VsAI,
 		MoveCount:            g.MoveCount,
 		EndReason:            g.EndReason,
 		Seats:                seats,

gateway/internal/transcode/transcode.go

@@ -246,7 +246,7 @@ func gameStateHandler(backend *backendclient.Client) Handler {
 func enqueueHandler(backend *backendclient.Client) Handler {
 	return func(ctx context.Context, req Request) ([]byte, error) {
 		in := fb.GetRootAsEnqueueRequest(req.Payload, 0)
-		m, err := backend.Enqueue(ctx, req.UserID, string(in.Variant()), in.MultipleWordsPerTurn())
+		m, err := backend.Enqueue(ctx, req.UserID, string(in.Variant()), in.MultipleWordsPerTurn(), in.VsAi())
 		if err != nil {
 			return nil, err
 		}