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/server/dto_test.go

@@ -25,6 +25,7 @@ func TestStatusForError(t *testing.T) {
 		"nudge own turn": {social.ErrNudgeOnOwnTurn, http.StatusConflict, "nudge_own_turn"},
 		"nudge too soon": {social.ErrNudgeTooSoon, http.StatusConflict, "nudge_too_soon"},
 		"chat off turn":  {social.ErrChatNotYourTurn, http.StatusConflict, "chat_not_your_turn"},
+		"chat one/turn":  {social.ErrChatAlreadySentThisTurn, http.StatusConflict, "chat_already_sent"},
 		"illegal play":   {engine.ErrIllegalPlay, http.StatusUnprocessableEntity, "illegal_play"},
 		"email taken":    {account.ErrEmailTaken, http.StatusConflict, "email_taken"},
 		"code mismatch":  {account.ErrCodeMismatch, http.StatusUnauthorized, "code_invalid"},

backend/internal/server/handlers.go

@@ -213,6 +213,8 @@ func statusForError(err error) (int, string) {
 		return http.StatusConflict, "nudge_too_soon"
 	case errors.Is(err, social.ErrChatNotYourTurn):
 		return http.StatusConflict, "chat_not_your_turn"
+	case errors.Is(err, social.ErrChatAlreadySentThisTurn):
+		return http.StatusConflict, "chat_already_sent"
 	case errors.Is(err, social.ErrSelfRelation):
 		return http.StatusBadRequest, "self_relation"
 	case errors.Is(err, social.ErrRequestExists):