docs(telegram): invert chat-gate strategy in docs; tune logs; i18n text

- Bake the final default-allow + mute-the-ineligible strategy into
  docs/ARCHITECTURE.md, docs/FUNCTIONAL.md (+_ru), platform/telegram/README.md,
  the deploy compose comment and the PRERELEASE tracker. The live test proved a
  per-user grant cannot exceed a deny-by-default group (Telegram intersects the
  chat default with the per-user permission), so the chat allows sending by
  default and the bot restricts the ineligible instead of granting the eligible.
- Lower the per-event chat_member trace and eligibility evaluation to Debug;
  keep the actual mute/unmute actions, the startup self-check and warnings at
  Info, so prod logs only what the bot did.
- Update game.searchingForOpponent (Searching -> Waiting for opponent / Поиск ->
  Ждём соперника) and the quickmatch e2e assertions to match.

platform/telegram/README.md

@@ -43,15 +43,19 @@ Telegram identity to an account from a browser. Both map a rejection to gRPC
   code. This is **self-contained** — the bot never calls back into the game, so `/start`
   onboarding works even when the game is down.
 - **Moderated-chat gating.** When `TELEGRAM_CHAT_ID` names a channel's linked discussion
-  group, the bot gates who may write there. The group is configured **default no-send**
-  (a human setting); the bot grants write access to a user who **joins** when they are
-  registered and neither admin-suspended nor `chat_muted`, asking the gateway over the
-  bot-link (`ResolveChatEligibility`). When an operator blocks/unblocks an account or
-  toggles its `chat_muted` role, the gateway pushes a `ChatGate` command and the bot
-  applies it — but only to a member currently in the chat (it probes one user with
-  `getChatMember`, since bots cannot list members). The bot must be an **administrator**
-  there with the **"Ban users"** right (the Bot API `can_restrict_members`), and it
-  subscribes to `chat_member` updates, which Telegram delivers only to a chat admin.
+  group, the bot gates who may write there. The group **allows sending by default** (a
+  human setting) and the bot only **restricts** — Telegram intersects the chat default with
+  each user's permission, so a per-user grant cannot exceed a deny-by-default group, and the
+  gate must mute the ineligible rather than grant the eligible. On a `chat_member` event the
+  bot asks the gateway (`ResolveChatEligibility`) and **mutes** a member who is not registered
+  or is admin-suspended or `chat_muted`, **un-mutes** an eligible one it had muted, and leaves
+  an already-allowed eligible member untouched (it acts only when the state differs, so it is
+  idempotent and skips its own change). When an operator blocks/unblocks an account, toggles
+  its `chat_muted` role, or a user first registers, the gateway pushes a `ChatGate` command and
+  the bot applies it — but only to a member currently in the chat (it probes one user with
+  `getChatMember`, since bots cannot list members). The bot must be an **administrator** there
+  with the **"Ban users"** right (the Bot API `can_restrict_members`), and it subscribes to
+  `chat_member` updates, which Telegram delivers only to a chat admin.
 - **Promo bot (optional).** When `TELEGRAM_PROMO_BOT_TOKEN` is set, the container also
   runs a **second, standalone** bot whose only job is to answer `/start` with a localized
   message and a button that opens the **main** bot's Mini App. The button is a **URL** to