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.

PLAN.md

@@ -583,6 +583,18 @@ Open details: deployment target/host; dashboards; load expectations.
     REST handlers under `/api/v1/user/{friends,blocks,invitations,profile,email,stats}`
     and `…/games/:id/gcg`. UI grows to ~82 KB gzip JS (budget 100 KB). No CI workflow
     change (the Go and UI workflows already cover the new code).
+  - **UI polish (owner review follow-up)**: a copyable friend code (📋 + toast); the
+    lobby notification badge fixed (it had inherited the hamburger-bar style) and made
+    a proper count dot; Safari flex inputs given `min-width:0`; **profile-edit
+    validation on both UI and backend** — display-name format (letters + single
+    `␠`/`.`/`_`, ≤ 32 runes), a **UTC-offset** timezone picker (`account.ResolveZone`
+    parses `±HH:MM` or IANA; DST is traded for the simple picker), a 10-minute away grid
+    capped at **12 h** (wrap-aware), email format — with Save disabled and invalid
+    fields red-bordered while any field is invalid; language stays in Settings; in a
+    game, an "add to friends" item flips to a disabled "request sent"; chat send/nudge
+    became ⬆️/🛎️ icons; a **finished game** drops its last-word highlight, hides Check
+    word / Drop game, disables zoom, and draws an **inert footer** (greyed rack + tab
+    bar) instead of hiding it.
 
 ## Deferred TODOs (cross-stage)