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/stats.test.ts

@@ -1,5 +1,5 @@
 import { describe, expect, it } from 'vitest';
-import { gamesPlayed, winRate } from './stats';
+import { gamesPlayed, hintSharePercent, winRate } from './stats';
 import type { Stats } from './model';
 
 const s = (wins: number, losses: number, draws: number): Stats => ({
@@ -8,8 +8,14 @@ const s = (wins: number, losses: number, draws: number): Stats => ({
   draws,
   maxGamePoints: 0,
   maxWordPoints: 0,
+  moves: 0,
+  hintsUsed: 0,
+  bestMoves: [],
 });
 
+// withCounts overrides moves/hintsUsed on the zero fixture for the hint-share cases.
+const withCounts = (moves: number, hintsUsed: number): Stats => ({ ...s(0, 0, 0), moves, hintsUsed });
+
 describe('stats', () => {
   it('sums games played', () => {
     expect(gamesPlayed(s(7, 4, 1))).toBe(12);
@@ -23,4 +29,14 @@ describe('stats', () => {
   it('win rate is 0 with no games', () => {
     expect(winRate(s(0, 0, 0))).toBe(0);
   });
+
+  it('computes the hint share (hints / plays)', () => {
+    expect(hintSharePercent(withCounts(200, 10))).toBe(5); // 10/200 = 5%
+    expect(hintSharePercent(withCounts(248, 12))).toBeCloseTo(4.8387, 3);
+  });
+
+  it('hint share is 0 with no plays (no division by zero)', () => {
+    expect(hintSharePercent(withCounts(0, 0))).toBe(0);
+    expect(hintSharePercent(withCounts(0, 5))).toBe(0);
+  });
 });