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/src/lib/mock/client.ts

@@ -295,7 +295,10 @@ export class MockGateway implements GatewayClient {
       seat: this.mySeat(g),
       rack: [...g.rack],
       bagLen: g.bagLen,
-      hintsRemaining: g.hintsRemaining,
+      // g.hintsRemaining is the per-game allowance; the wallet is the shared profile balance.
+      // hints_remaining folds the two together (as the backend does), walletBalance is the wallet.
+      hintsRemaining: g.hintsRemaining + this.profile.hintBalance,
+      walletBalance: this.profile.hintBalance,
     };
   }
 
@@ -395,8 +398,11 @@ export class MockGateway implements GatewayClient {
 
   async hint(gameId: string): Promise<HintResult> {
     const g = this.game(gameId);
-    if (g.hintsRemaining <= 0) throw new GatewayError('hint_unavailable');
-    g.hintsRemaining -= 1;
+    if (g.hintsRemaining <= 0 && this.profile.hintBalance <= 0) throw new GatewayError('hint_unavailable');
+    // Spend the per-game allowance first, then the shared wallet — mirroring the backend, so a
+    // wallet hint in one game lowers the count shown in every other game (the bug this fixes).
+    if (g.hintsRemaining > 0) g.hintsRemaining -= 1;
+    else this.profile.hintBalance -= 1;
     const letter = g.rack.find((l) => l !== '?') ?? 'A';
     return {
       move: {
@@ -411,7 +417,8 @@ export class MockGateway implements GatewayClient {
         score: valueForLetter(g.view.variant, letter),
         total: 0,
       },
-      hintsRemaining: g.hintsRemaining,
+      hintsRemaining: g.hintsRemaining + this.profile.hintBalance,
+      walletBalance: this.profile.hintBalance,
     };
   }