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.

docs/UI_DESIGN.md

@@ -248,7 +248,10 @@ IV 🏅; active games show Your move 🟢 / Opponent's move ⏳; invitations use
 - **Finished game**: the board keeps no last-word highlight and no zoom; the history header
   offers *Export GCG* (not *Drop game*) and the comms hub hides the 🔎 *Dictionary* tab; and
   the footer (rack + tab bar) is **drawn but inert** (greyed, non-interactive) rather than
-  hidden, so the layout does not jump. Chat send / nudge are the ⬆️ / 🛎️ icons.
+  hidden, so the layout does not jump. Chat send / nudge are the ⬆️ / 🛎️ icons. The input
+  row is turn-driven: on your turn the message field shows until your one allowed message is
+  sent, then a short caption replaces it until the next turn; on the opponent's turn the 🛎️
+  nudge takes the field's place.
 
 ## Caveat