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/game.spec.ts

@@ -66,7 +66,7 @@ test('a placed tile is saved as a draft and restored on reopening the game', asy
 test('new game: variant buttons show a rules summary and the move-limit', async ({ page }) => {
   await page.goto('/');
   await page.getByRole('button', { name: /guest/i }).click();
-  await page.getByRole('button', { name: /New/ }).click(); // lobby tab bar -> auto-match
+  await page.getByRole('button', { name: /🎲/ }).click(); // lobby tab bar -> auto-match
   await expect(page.locator('.vrules').first()).toBeVisible(); // per-variant rules summary
   await expect(page.locator('.movelimit')).toBeVisible(); // turn-time under the buttons
 });
@@ -74,7 +74,7 @@ test('new game: variant buttons show a rules summary and the move-limit', async
 test('new game: auto-match shows the off-by-default rule toggle from the start (no layout jump on selection)', async ({ page }) => {
   await page.goto('/');
   await page.getByRole('button', { name: /guest/i }).click();
-  await page.getByRole('button', { name: /New/ }).click(); // auto-match
+  await page.getByRole('button', { name: /🎲/ }).click(); // auto-match
   // Several variants are offered, so nothing is selected: Start is disabled. The rule toggle is shown
   // from the start (a Russian variant is available), so selecting one does not shift the layout.
   const start = page.getByRole('button', { name: /Start game/i });