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/inttest/social_test.go

@@ -333,6 +333,29 @@ func TestChatOnlyOnYourTurn(t *testing.T) {
 	}
 }
 
+// TestChatOnePerTurn checks the one-message-per-turn limit: a second message on the same
+// turn is refused, and a fresh turn (turn_started_at advancing past the sent message)
+// reopens chat for the player.
+func TestChatOnePerTurn(t *testing.T) {
+	ctx := context.Background()
+	svc := newSocialService()
+	gameID, seats := newGameWithSeats(t, 2) // seat 0 is to move at the opening
+	if _, err := svc.PostMessage(ctx, gameID, seats[0], "first", ""); err != nil {
+		t.Fatalf("first message: %v", err)
+	}
+	if _, err := svc.PostMessage(ctx, gameID, seats[0], "second", ""); !errors.Is(err, social.ErrChatAlreadySentThisTurn) {
+		t.Fatalf("second message = %v, want ErrChatAlreadySentThisTurn", err)
+	}
+	// Advancing the turn start past the sent message (as a real move does) reopens chat.
+	if _, err := testDB.ExecContext(ctx,
+		`UPDATE backend.games SET turn_started_at = now() WHERE game_id = $1`, gameID); err != nil {
+		t.Fatalf("advance turn: %v", err)
+	}
+	if _, err := svc.PostMessage(ctx, gameID, seats[0], "next turn", ""); err != nil {
+		t.Fatalf("message on the new turn: %v", err)
+	}
+}
+
 func TestNudgeRulesAndRateLimit(t *testing.T) {
 	ctx := context.Background()
 	svc := newSocialService()