Stage 8 polish: profile validation, finished-game UI, badge + Safari fixes

Owner-review follow-up on the Stage 8 branch:
- Friend code is copyable (📋 + toast). The lobby notification badge is fixed —
  it had inherited the hamburger-bar style — into a proper round count dot.
- Safari: min-width:0 on flex text inputs (friend code, profile, chat) so they
  shrink instead of pushing the adjacent button off-screen.
- Profile editing is validated on both the UI and the backend: display-name format
  (letters joined by single space/./_ separators, no leading/trailing/adjacent
  separators, <=32 runes), a UTC-offset timezone picker (account.ResolveZone parses
  ±HH:MM or a legacy IANA name), a 10-minute away grid capped at 12h (wrap-aware),
  and email format; Save is disabled and invalid fields red-bordered until valid.
  Language stays in Settings.
- In a game, an "add to friends" menu item flips to a disabled "request sent"; chat
  send/nudge became ⬆️/🛎️ icon buttons.
- A finished game drops its last-word highlight, hides Check word / Drop game,
  disables zoom, and draws an inert (greyed) footer instead of hiding it.

Tests: account validators (name/away/zone), UI profileValidation, e2e for the
finished-game footer/menu and the copy control. Docs (PLAN, ARCHITECTURE,
FUNCTIONAL +ru, UI_DESIGN) updated for the display-name rule, UTC-offset timezone
and the 12h away window.

docs/ARCHITECTURE.md

@@ -298,11 +298,15 @@ requires (there is no DM surface; chat is per-game).
   the opponent may nudge **once per hour per game**; it is not allowed on one's own
   turn. The platform-native delivery is wired with the gateway / platform
   side-service (Stage 6 / 8).
-- **Profile**: `preferred_language` (en/ru), display name, email
-  (confirm-code binding, see §4), **timezone** (drives the away window and the
-  robot's sleep; user-editable), the daily **away window** and the block toggles —
-  all editable through `account.UpdateProfile`. Linked platform accounts and merge
-  are Stage 11.
+- **Profile**: `preferred_language` (en/ru, edited in Settings), display name, email
+  (confirm-code binding, see §4), **timezone**, the daily **away window** and the
+  block toggles — all editable through `account.UpdateProfile`, which validates them
+  (Stage 8): a display name is Unicode letters joined by single ` `/`.`/`_`
+  separators (no leading/trailing/adjacent separators, ≤ 32 runes); the timezone is a
+  fixed `±HH:MM` **UTC offset** (or a legacy IANA name) resolved by `account.ResolveZone`
+  for the sweeper and the robot's sleep (a fixed offset trades DST for a simple
+  picker); the away window is at most **12 h** (midnight-wrap aware). Linked platform
+  accounts and merge are Stage 11.
 
 ## 9. Persistence