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.

ui/e2e/social.spec.ts

@@ -230,7 +230,7 @@ test('link account: the Telegram web sign-in control is offered in a browser', a
   await expect(page.getByRole('button', { name: 'Link Telegram' })).toBeVisible();
 });
 
-test('chat: the message field shows on your turn, the nudge replaces it otherwise', async ({ page }) => {
+test('chat: one message per turn — the field shows, then a caption replaces it after sending', async ({ page }) => {
   await loginLobby(page);
   await page.getByRole('button', { name: /Ann/ }).click(); // g1: your turn
   await page.locator('.scoreboard').click(); // open the history
@@ -241,4 +241,11 @@ test('chat: the message field shows on your turn, the nudge replaces it otherwis
   // through the aria-label.
   await expect(page.getByRole('button', { name: 'Send' })).toBeVisible();
   await expect(page.getByRole('button', { name: 'Nudge' })).toHaveCount(0);
+  // The limit is one message per turn: after sending, the field is hidden behind a caption.
+  // It is still your turn, so the nudge does not appear either.
+  await page.getByPlaceholder(/Quick message/).fill('hi there');
+  await page.getByRole('button', { name: 'Send' }).click();
+  await expect(page.getByText('You can write again next turn.')).toBeVisible();
+  await expect(page.getByRole('button', { name: 'Send' })).toHaveCount(0);
+  await expect(page.getByRole('button', { name: 'Nudge' })).toHaveCount(0);
 });