fix(hint): stop the hint count going stale across games

The in-game hint badge re-fetched on entry and, for a game where it was the
player's turn, showed a too-high count that "reset" (e.g. back to 11) — the
wallet hint spent in another game was not reflected.

Root cause: the server sends one hints_remaining = per-game allowance + global
wallet, and the client cached that combined number per game. The wallet is
global, so spending a wallet hint in one game left every other game's cached
count stale (a my-turn game holds the stalest value: the opponent-moved delta
preserves the old number, whereas a game you just moved in re-cached a fresh
one). The backend allowance-then-wallet spend order was already correct.

Fix: split the two. StateView/HintResult gain a trailing wallet_balance field
(the global wallet alone); the client derives the per-game allowance as
hints_remaining - wallet_balance (stable, cacheable) and reads the wallet live
from the profile, refreshing it from every state/hint response. The badge is
allowance + live wallet, so a wallet hint anywhere updates every game at once.

- wire: scrabble.fbs StateView/HintResult + pkg/wire.BuildStateView (the single
  encoder for both the gateway transcode and the backend's event StateView),
  gateway encode + resp structs, regen.
- backend: game StateView/HintResult + service (GameState/Hint) + eventwire +
  notify PlayerState/encode + server DTOs.
- ui: lib/hints.ts (pure hintsLeft), Game.svelte (badge + syncWallet on
  load/hint, carry wallet_balance through applyMoveResult), codec/model, mock.
- docs: ARCHITECTURE §Hint.

Tests: hints.ts unit (incl. the staleness case), TestHintPolicy extended
(wallet_balance + allowance-first), gateway state/hint round-trips.

ui/src/lib/gamedelta.test.ts

@@ -27,7 +27,7 @@ function move(player: number): MoveRecord {
 }
 
 function cache(moveCount: number, seat = 0, over = false): CachedGame {
-  const view: StateView = { game: gameView(moveCount, over), seat, rack: ['a', 'b'], bagLen: 50, hintsRemaining: 1 };
+  const view: StateView = { game: gameView(moveCount, over), seat, rack: ['a', 'b'], bagLen: 50, hintsRemaining: 1, walletBalance: 0 };
   return { view, moves: [] };
 }
 
@@ -37,7 +37,7 @@ function delta(moveCount: number, player: number, bagLen = 47): MoveDelta {
 
 describe('seedInitialState', () => {
   it('wraps an initial view with an empty journal', () => {
-    const view: StateView = { game: gameView(0), seat: 1, rack: ['x'], bagLen: 80, hintsRemaining: 2 };
+    const view: StateView = { game: gameView(0), seat: 1, rack: ['x'], bagLen: 80, hintsRemaining: 2, walletBalance: 0 };
     expect(seedInitialState(view)).toEqual({ view, moves: [] });
   });
 });
@@ -152,12 +152,12 @@ describe('applyOpponentJoined', () => {
       { seat: 0, accountId: 'me', displayName: 'Me', score: 0, hintsUsed: 0, isWinner: false },
       { seat: 1, accountId: 'opp', displayName: 'Opp', score: 0, hintsUsed: 0, isWinner: false },
     ] };
-    return { game, seat: 0, rack: ['x'], bagLen: 90, hintsRemaining: 0 };
+    return { game, seat: 0, rack: ['x'], bagLen: 90, hintsRemaining: 0, walletBalance: 0 };
   }
 
   it("adopts the joined seats and status while preserving the cached rack and moves", () => {
     // The cached open game is still "searching": empty seats, status open, the starter's own rack.
-    const cached: CachedGame = { view: { game: { ...gameView(2), status: 'open', seats: [] }, seat: 0, rack: ['a', 'b'], bagLen: 50, hintsRemaining: 1 }, moves: [move(0)] };
+    const cached: CachedGame = { view: { game: { ...gameView(2), status: 'open', seats: [] }, seat: 0, rack: ['a', 'b'], bagLen: 50, hintsRemaining: 1, walletBalance: 0 }, moves: [move(0)] };
     const res = applyOpponentJoined(cached, joinedState());
     expect(res?.view.game.status).toBe('active');
     expect(res?.view.game.seats).toHaveLength(2);