feat(chat): limit in-game chat to one message per turn

Enforce one chat message per turn on both ends. The backend rejects a
second message in the same turn (ErrChatAlreadySentThisTurn -> 409
chat_already_sent), keyed on the move-driven turn start (turn_started_at).
The UI derives "already wrote this turn" from the message list against
GameView.lastActivityUnix (no counter, survives reopening, resets on turn
change), hides the field behind a short caption once the limit is reached,
and now reloads the game state on turn/game-state events so the toggle and
the limit follow the live game. Enter is gated on !busy to avoid a
double-send in the in-flight window.

Backend: new game.TurnStartedAt; social GameReader gains it; PostMessage
enforces the limit reusing lastMessageAt. UI: new lib/chatlimit.ts pure
logic + unit tests; Chat/ChatScreen wiring; chat.sentThisTurn and
error.chat_already_sent i18n (en/ru); extended chat e2e. Docs: FUNCTIONAL
(+ru), ARCHITECTURE, UI_DESIGN.

backend/internal/social/chat.go

@@ -65,6 +65,18 @@ func (svc *Service) PostMessage(ctx context.Context, gameID, senderID uuid.UUID,
 	if idx != toMove {
 		return Message{}, ErrChatNotYourTurn
 	}
+	// At most one chat message per turn. The turn's start (move-driven, so stable for the
+	// whole turn) bounds the window: a prior message posted at or after it closes chat until
+	// the next turn.
+	turnStart, err := svc.games.TurnStartedAt(ctx, gameID)
+	if err != nil {
+		return Message{}, err
+	}
+	if last, ok, err := svc.store.lastMessageAt(ctx, gameID, senderID); err != nil {
+		return Message{}, err
+	} else if ok && !last.Before(turnStart) {
+		return Message{}, ErrChatAlreadySentThisTurn
+	}
 	sender, err := svc.accounts.GetByID(ctx, senderID)
 	if err != nil {
 		return Message{}, err

backend/internal/social/social.go

@@ -31,6 +31,10 @@ type GameReader interface {
 	// LastMoveAt is the time of an account's most recent move in a game (and whether it
 	// has moved); the nudge cooldown resets once the player has taken a turn.
 	LastMoveAt(ctx context.Context, gameID, accountID uuid.UUID) (time.Time, bool, error)
+	// TurnStartedAt is the start time of the game's current turn; it bounds the
+	// one-chat-message-per-turn limit (a message counts toward the current turn when it
+	// was posted at or after this time).
+	TurnStartedAt(ctx context.Context, gameID uuid.UUID) (time.Time, error)
 	// 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)
@@ -77,6 +81,9 @@ var (
 	// sender's turn — chat is allowed only on your own turn (the opponent's-turn control
 	// is the nudge).
 	ErrChatNotYourTurn = errors.New("social: cannot chat while it is not your turn")
+	// ErrChatAlreadySentThisTurn is returned when the sender has already posted a chat
+	// message during the current turn — at most one message is allowed per turn.
+	ErrChatAlreadySentThisTurn = errors.New("social: already sent a chat message this turn")
 )
 
 // Service is the social domain. It is the only writer of the friendships, blocks