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/game/Game.svelte

@@ -18,6 +18,7 @@
   import { centre, premiumGrid } from '../lib/premiums';
   import { variantNameKey } from '../lib/variants';
   import { alphabetLetters, hasAlphabet } from '../lib/alphabet';
+  import { hintsLeft } from '../lib/hints';
   import { shareOrDownloadGcg } from '../lib/share';
   import { getCachedGame, setCachedGame, setCachedDraft, type CachedGame } from '../lib/gamecache';
   import { patchLobbyGame } from '../lib/lobbycache';
@@ -132,6 +133,10 @@
   const playable = $derived(!!view && (view.game.status === 'active' || view.game.status === 'open'));
   const isMyTurn = $derived(!!view && playable && view.game.toMove === view.seat);
   const gameOver = $derived(!!view && view.game.status === 'finished');
+  // The hint badge: this game's allowance remaining plus the LIVE global wallet. Reading the
+  // wallet from the profile (not the per-game view snapshot) keeps it correct after a wallet
+  // hint was spent in another game (see lib/hints).
+  const hintCount = $derived(hintsLeft(view, app.profile?.hintBalance ?? 0));
   // RACK_SIZE mirrors the engine's rules.RackSize (7 for every current variant). The exchange
   // gate is only a UX guard: the backend stays the source of truth and rejects an under-supplied
   // exchange regardless (engine rejects when bag.Len() < rules.RackSize).
@@ -154,6 +159,13 @@
     return MOVE_LABELS.has(action) ? t(`move.${action}` as MessageKey) : action;
   }
 
+  // syncWallet adopts the server's authoritative hint-wallet balance into the global profile.
+  // The wallet is global, so keeping it live here (rather than per-game) is what stops the hint
+  // badge from going stale when a wallet hint was spent in another game.
+  function syncWallet(walletBalance: number) {
+    if (app.profile) app.profile.hintBalance = walletBalance;
+  }
+
   async function load() {
     try {
       // Ask for the alphabet table only on a per-variant cache miss (the first open of a
@@ -167,6 +179,7 @@
         gateway.draftGet(id).catch(() => ''),
       ]);
       view = st;
+      syncWallet(st.walletBalance);
       // Seed the unread flag from the authoritative state (the live stream only raises it).
       seedChatUnread(id, st.game.unreadChat);
       moves = hist.moves;
@@ -615,7 +628,16 @@
   // applyMoveResult renders the actor's own just-committed move from the response — the move, the
   // post-move game and the refilled rack — without a follow-up game.state + game.history.
   function applyMoveResult(r: MoveResult) {
-    view = { game: r.game, seat: r.move.player, rack: r.rack, bagLen: r.bagLen, hintsRemaining: view?.hintsRemaining ?? 0 };
+    view = {
+      game: r.game,
+      seat: r.move.player,
+      rack: r.rack,
+      bagLen: r.bagLen,
+      // A move is not a hint, so the per-game allowance and the wallet are unchanged: carry both
+      // forward (their difference is the stable allowance; the badge adds the live wallet).
+      hintsRemaining: view?.hintsRemaining ?? 0,
+      walletBalance: view?.walletBalance ?? 0,
+    };
     // The move result is an authoritative per-viewer view: a nudge the actor just answered by
     // moving is already cleared server-side, so reconcile the unread flag from it.
     seedChatUnread(id, r.game.unreadChat);
@@ -698,7 +720,8 @@
           recenter++;
         }
         if (isCoarse()) zoomed = true;
-        view = { ...view, hintsRemaining: h.hintsRemaining };
+        view = { ...view, hintsRemaining: h.hintsRemaining, walletBalance: h.walletBalance };
+        syncWallet(h.walletBalance);
         recompute();
       }
     } catch (e) {
@@ -1067,7 +1090,7 @@
     <div class="status">
       <span>{view.bagLen === 0 ? t('game.bagEmpty') : t('game.bag', { n: view.bagLen })}</span>
       {#if gameOver}
-        <strong class="over">{t('game.over')} — {resultText()}</strong>
+        <strong class="over">{resultText()}</strong>
       {:else if placement.pending.length === 0}
         <span class="turn-ind">{isMyTurn ? t('game.yourTurn') : turnLabel()}</span>
       {/if}
@@ -1107,10 +1130,10 @@
   <TapConfirm
     triggerClass="tab"
     label={t('game.hint')}
-    disabled={busy || !isMyTurn || !connection.online || (view?.hintsRemaining ?? 0) <= 0}
+    disabled={busy || !isMyTurn || !connection.online || hintCount <= 0}
     onconfirm={doHint}
   >
-    <span class="sq">🛟{#if (view?.hintsRemaining ?? 0) > 0}<span class="badge">{view?.hintsRemaining}</span>{/if}</span>
+    <span class="sq">🛟{#if hintCount > 0}<span class="badge">{hintCount}</span>{/if}</span>
     <span class="lbl">{t('game.hint')}</span>
   </TapConfirm>
   {#if placement.pending.length > 0}