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.

ui/src/game/Chat.svelte

@@ -46,8 +46,8 @@
       bind:value={text}
       onkeydown={(e) => e.key === 'Enter' && send()}
     />
-    <button onclick={send} disabled={busy}>{t('chat.send')}</button>
-    <button class="nudge" onclick={onnudge} disabled={busy}>{t('chat.nudge')}</button>
+    <button class="iconbtn" onclick={send} disabled={busy} aria-label={t('chat.send')}>⬆️</button>
+    <button class="iconbtn" onclick={onnudge} disabled={busy} aria-label={t('chat.nudge')}>🛎️</button>
   </div>
 </div>
 
@@ -95,18 +95,21 @@
   }
   .input input {
     flex: 1;
+    min-width: 0;
     padding: 10px;
     border: 1px solid var(--border);
     border-radius: var(--radius-sm);
     background: var(--bg);
     color: var(--text);
   }
-  .input button {
-    padding: 10px 12px;
+  .iconbtn {
+    flex: 0 0 auto;
+    padding: 8px 12px;
     border: 1px solid var(--border);
     background: var(--surface);
     color: var(--text);
     border-radius: var(--radius-sm);
-    font-weight: 600;
+    font-size: 1.25rem;
+    line-height: 1;
   }
 </style>