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.

backend/internal/notify/encode.go

@@ -36,6 +36,7 @@ func toWireGame(g GameSummary) wire.GameView {
 		ToMove:               g.ToMove,
 		TurnTimeoutSecs:      g.TurnTimeoutSecs,
 		MultipleWordsPerTurn: g.MultipleWordsPerTurn,
+		VsAI:                 g.VsAI,
 		MoveCount:            g.MoveCount,
 		EndReason:            g.EndReason,
 		Seats:                seats,

backend/internal/notify/payload.go

@@ -29,10 +29,12 @@ type GameSummary struct {
 	ToMove               int
 	TurnTimeoutSecs      int
 	MultipleWordsPerTurn bool
-	MoveCount            int
-	EndReason            string
-	Seats                []SeatStanding
-	LastActivityUnix     int64
+	// VsAI marks an honest-AI game (the opponent is shown as 🤖, chat/nudge/add-friend off).
+	VsAI             bool
+	MoveCount        int
+	EndReason        string
+	Seats            []SeatStanding
+	LastActivityUnix int64
 }
 
 // AlphabetLetter is one variant alphabet entry (a display-only row) embedded in an