docs: bake Telegram invite & launch refinements into ARCHITECTURE/UI_DESIGN

- UI_DESIGN: mobile immersive fullscreen on launch (desktop keeps full-size); the
  close confirmation is now mobile-only; friend-code share-via-Telegram deep-link
  (per-bot, by service language), the friendly self-redeem note, and the
  outdated-link lobby notice.
- ARCHITECTURE: the service language rides the Session wire so the client builds
  the per-bot invite link; the friend code is shared as a startapp deep-link with
  graceful spent/expired handling.

docs/ARCHITECTURE.md

@@ -151,7 +151,9 @@ arrive from a platform rather than completing a mandatory registration).
   login — last-login-wins) and routes the user's out-of-app push back through the right
   bot (§10) — **except a game event, which routes by the game's own language** (its variant →
   en/ru), so a game's notification always comes from the game's bot rather than the
-  recipient's latest login bot. The service language is distinct from `preferred_language` (the
+  recipient's latest login bot. It also rides the **Session wire** to the client, which uses it
+  to build the friend-invite **share link** (and its caption) for the **same bot** the player
+  is in. The service language is distinct from `preferred_language` (the
   interface language) and from a game's variant language. Non-Telegram logins (web / email / guest) carry the
   gateway's default set (`GATEWAY_DEFAULT_SUPPORTED_LANGUAGES`, all variants by default).
 - The client holds `session_id` in memory for the app session (browser/OS
@@ -425,7 +427,11 @@ English game the Latin pool.
 - **Friends**: two add paths over one `friendships` table. A **one-time
   code** the to-be-added player issues (a `friend_codes` row: 6-digit numeric,
   SHA-256-hashed, **12 h** TTL, one live code per issuer, single-use, redeem
-  rate-limited) is redeemed by the other player to become friends immediately.
+  rate-limited) is redeemed by the other player to become friends immediately. It is shared as
+  a Telegram `startapp` deep-link to the issuer's own bot (by service language, with a matching
+  caption), redeemed by the recipient's Mini App on launch; a **spent or expired** code is not
+  surfaced as an error there but lands the visitor in the lobby with a gentle pointer to the
+  right bot, since the shared link outlives the single-use code.
   Alternatively a **request → accept** is sent to someone you **share a game with**
   (active or finished); the recipient may accept, ignore (the pending row lazily
   expires after **30 days** and may be re-sent), or **decline** — a decline is