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/social/chat.go

@@ -62,6 +62,12 @@ func (svc *Service) PostMessage(ctx context.Context, gameID, senderID uuid.UUID,
 	if status != statusActive {
 		return Message{}, ErrGameNotActive
 	}
+	// Chat is disabled in honest-AI games (the opponent is a robot).
+	if vsAI, err := svc.games.VsAI(ctx, gameID); err != nil {
+		return Message{}, err
+	} else if vsAI {
+		return Message{}, ErrGameVsAI
+	}
 	if idx != toMove {
 		return Message{}, ErrChatNotYourTurn
 	}
@@ -118,6 +124,12 @@ func (svc *Service) Nudge(ctx context.Context, gameID, senderID uuid.UUID) (Mess
 	if idx < 0 {
 		return Message{}, ErrNotParticipant
 	}
+	// Nudge is disabled in honest-AI games (the opponent is a robot).
+	if vsAI, err := svc.games.VsAI(ctx, gameID); err != nil {
+		return Message{}, err
+	} else if vsAI {
+		return Message{}, ErrGameVsAI
+	}
 	if idx == toMove {
 		return Message{}, ErrNudgeOnOwnTurn
 	}

backend/internal/social/social.go

@@ -38,6 +38,9 @@ type GameReader interface {
 	// GameLanguage is the game's language tag ("en"/"ru"), so a nudge's out-of-app push routes
 	// to the game's bot rather than the recipient's last-login bot.
 	GameLanguage(ctx context.Context, gameID uuid.UUID) (string, error)
+	// VsAI reports whether the game is an honest-AI game, in which chat and nudge are
+	// both disabled (the game still reports status 'active').
+	VsAI(ctx context.Context, gameID uuid.UUID) (bool, error)
 }
 
 // Sentinel errors returned by the service.
@@ -77,6 +80,9 @@ var (
 	ErrNudgeTooSoon = errors.New("social: a nudge was already sent in the last hour")
 	// ErrGameNotActive is returned when a nudge is attempted on a finished game.
 	ErrGameNotActive = errors.New("social: game is not active")
+	// ErrGameVsAI is returned when chat or nudge is attempted in an honest-AI game,
+	// where both are disabled (the UI also disables the controls).
+	ErrGameVsAI = errors.New("social: chat and nudge are disabled in AI games")
 	// ErrChatNotYourTurn is returned when a chat message is sent while it is not the
 	// sender's turn — chat is allowed only on your own turn (the opponent's-turn control
 	// is the nudge).