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/ARCHITECTURE.md

@@ -444,7 +444,10 @@ English game the Latin pool.
 - **Chat**: per-game, persisted (kept with the game's archive), **≤ 60 runes**,
   and **validated on input** — links, email addresses and phone numbers (including
   lightly obfuscated forms) are rejected, since the chat is for quick reactions,
-  not contact exchange. Each message stores the sender's IP (forwarded by the
+  not contact exchange. Chat is allowed **only on the sender's own turn** and
+  **at most once per turn** (the turn boundary is the move-driven turn start; the
+  opponent's-turn control is the nudge); the backend enforces both and the client
+  mirrors them by hiding the field. Each message stores the sender's IP (forwarded by the
   gateway) for moderation. A sender who has disabled chat cannot post,
   and messages from a blocked sender are hidden from the viewer. The operator console
   has a **Messages** section that lists posted messages (nudges excluded)

docs/FUNCTIONAL.md

@@ -155,7 +155,9 @@ and/or friend requests — and block individual players (a per-user block hides
 person's chat and stops requests and game invitations both ways; it also ends any
 existing friendship). Per-game chat is for quick reactions: messages are short
 (up to 60 characters) and may not contain links, email addresses or phone numbers,
-even disguised. Nudge the player whose turn is awaited at most once per hour (the
+even disguised. You may send **one message per turn, on your own turn**; once it is sent
+the field gives way to a short caption until your next turn. Nudge the player whose turn
+is awaited at most once per hour (the
 nudge is part of the game chat); the out-of-app push is delivered via the platform.
 Chat and the word-check tool share one **comms screen** with **💬 chat** / **🔎 dictionary**
 tabs, reached from the 💬 in the move-history header (with a back to the game); a new chat

docs/FUNCTIONAL_ru.md

@@ -159,7 +159,9 @@ nudge) приходят от бота **этой партии** — по язы
 и блокировка конкретного игрока (пер-юзер блок скрывает его чат и запрещает заявки
 и приглашения в игру в обе стороны, а также расторгает уже имеющуюся дружбу). Чат
 партии — для быстрых реакций: сообщения короткие (до 60 символов) и не должны
-содержать ссылок, email и телефонов, даже завуалированных. Nudge ожидаемого
+содержать ссылок, email и телефонов, даже завуалированных. В свой ход можно отправить
+**одно сообщение за ход**; после отправки поле сменяется короткой подписью до следующего
+хода. Nudge ожидаемого
 соперника — не чаще раза в час (nudge — часть игрового чата); внеприложенческий
 push доставляется через платформу.
 Чат и инструмент проверки слова — один **экран связи** со вкладками **💬 чат** / **🔎 словарь**,

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