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/e2e/social.spec.ts

@@ -19,9 +19,10 @@ test('friends: issue a code, accept an incoming request, redeem a code', async (
   await loginLobby(page);
   await openFriends(page);
 
-  // Issue a one-time code — it is shown to share.
+  // Issue a one-time code — it is shown to share, with a copy control.
   await page.getByRole('button', { name: /Show my code/i }).click();
   await expect(page.getByTestId('friend-code')).toContainText('246813');
+  await expect(page.getByRole('button', { name: 'Copy' })).toBeVisible();
 
   // The seeded incoming request (Rick) can be accepted; the requests section clears.
   await expect(page.getByText('Friend requests')).toBeVisible();
@@ -73,3 +74,15 @@ test('GCG export is hidden for an active game', async ({ page }) => {
   await page.locator('.burger').first().click();
   await expect(page.getByRole('button', { name: /Export GCG/ })).toHaveCount(0);
 });
+
+test('finished game draws an inert footer and trims the live-only menu', async ({ page }) => {
+  await loginLobby(page);
+  await page.getByRole('button', { name: /Kaya/ }).click(); // finished game vs Kaya
+  await expect(page.locator('[data-cell]').first()).toBeVisible();
+  // The footer (tab bar) is drawn but its controls are disabled in a finished game.
+  await expect(page.locator('.tab').first()).toBeDisabled();
+  // The menu drops Check word and Drop game once the game is over.
+  await page.locator('.burger').first().click();
+  await expect(page.getByRole('button', { name: 'Check word' })).toHaveCount(0);
+  await expect(page.getByRole('button', { name: 'Drop game' })).toHaveCount(0);
+});