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