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/model.ts

@@ -67,13 +67,17 @@ export interface MoveRecord {
   total: number;
 }
 
-/** A seated player's private view of a game. */
+/** A seated player's private view of a game. hintsRemaining folds the per-game allowance
+ *  together with the global wallet; walletBalance is the wallet alone, so the client can
+ *  derive the per-game allowance (hintsRemaining - walletBalance) and keep the wallet live
+ *  across games (see lib/hints). */
 export interface StateView {
   game: GameView;
   seat: number;
   rack: string[];
   bagLen: number;
   hintsRemaining: number;
+  walletBalance: number;
 }
 
 export interface MoveResult {
@@ -87,6 +91,7 @@ export interface MoveResult {
 export interface HintResult {
   move: MoveRecord;
   hintsRemaining: number;
+  walletBalance: number;
 }
 
 export interface EvalResult {
@@ -206,13 +211,37 @@ export interface FriendCode {
   expiresAtUnix: number;
 }
 
-/** A durable account's lifetime statistics. */
+/** One letter cell of a best-move word: its display letter, its tile value (0 for a
+ *  blank) and whether it is a blank — enough to render it as a game tile without the
+ *  variant's alphabet table. */
+export interface BestMoveTile {
+  letter: string;
+  value: number;
+  blank: boolean;
+}
+
+/** An account's highest-scoring single play within one variant: the variant, the play's
+ *  total score and its main word as ordered tiles. */
+export interface BestMove {
+  variant: Variant;
+  score: number;
+  word: BestMoveTile[];
+}
+
+/** A durable account's lifetime statistics. bestMoves breaks the best move down per
+ *  variant (with the word itself); it is empty for an account with no recorded play and
+ *  lists only variants the account has played. */
 export interface Stats {
   wins: number;
   losses: number;
   draws: number;
   maxGamePoints: number;
   maxWordPoints: number;
+  /** Lifetime count of the player's plays (tile placements). */
+  moves: number;
+  /** Lifetime count of hints the player took (allowance + wallet). */
+  hintsUsed: number;
+  bestMoves: BestMove[];
 }
 
 /** Settings the inviter chooses for a friend game. */