feat(stats): best-move word, moves & hint-share, and a hint-count fix (#81)

The statistics screen gains real depth, plus a hint-count bug fix found along the way.

- Best move per variant: the screen shows the actual best-move word (drawn as game
  tiles; a wildcard shows its letter but no value), broken down by game variant, empty
  variants omitted. New account_best_move table, written at game finish.
- Moves & hint share: two new lifetime tiles — the player's play count and the share of
  plays that used a hint — from summed account_stats counters (moves, hints_used).
  Honest-AI games are excluded, like the rest of the stats.
- Hint-count fix: the in-game hint badge no longer goes stale across games. The global
  wallet now rides the wire apart from the per-game allowance (wallet_balance on
  StateView/HintResult/StatsView), so the client reads the live wallet rather than a
  per-game snapshot; game_players.hints_used now counts every hint (allowance + wallet),
  its true per-game total.
- Account merge: sums the new moves/hints_used counters and merges the per-variant best
  moves (higher score kept), which it previously dropped.
- Admin: the user card shows Moves and Hints used.
- UI polish: tab/label wording, game-over text, and e2e selectors hardened against label
  changes.

All wire additions are trailing (backward-compatible). Docs (ARCHITECTURE, FUNCTIONAL +ru,
UISN_DESIGN) updated in step.

ui/e2e/social.spec.ts

@@ -53,11 +53,19 @@ test('invitations: the lobby shows an invitation and accepting clears it', async
   await expect(page.getByText(/From Kaya/)).toBeHidden();
 });
 
-test('stats screen shows the metrics', async ({ page }) => {
+test('stats screen shows the metrics and the per-variant best move', async ({ page }) => {
   await loginLobby(page);
   await page.getByRole('button', { name: /Stats/ }).click();
   await expect(page.getByText('Win rate')).toBeVisible();
   await expect(page.getByText('Best move')).toBeVisible();
+  // The Moves count and the derived Hint share (12 hints / 248 plays = 4.8%, one decimal).
+  await expect(page.getByText('Moves', { exact: true })).toBeVisible();
+  await expect(page.getByText('Hint share')).toBeVisible();
+  await expect(page.getByText('4.8%')).toBeVisible();
+  // The best move breaks down per played variant, each row labelled by the variant and
+  // ending in the play's score (the word itself renders as game tiles).
+  await expect(page.getByText('Scrabble', { exact: true })).toBeVisible();
+  await expect(page.getByText('134')).toBeVisible();
 });
 
 test('settings hub: tabs switch in place and back returns to the lobby', async ({ page }) => {
@@ -158,7 +166,7 @@ test('lobby ⚙️ tab shows the pending friend-request count', async ({ page })
 
 test('play with friends: a game type is required to send an invitation', async ({ page }) => {
   await loginLobby(page);
-  await page.getByRole('button', { name: /New/ }).click(); // lobby tab bar
+  await page.getByRole('button', { name: /🎲/ }).click(); // lobby tab bar (New Game tab, by its 🎲 icon — the label is themeable)
   await page.getByRole('button', { name: 'Play with friends' }).click();
 
   const send = page.getByRole('button', { name: 'Send invitation' });