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/hints.ts

@@ -0,0 +1,26 @@
+// Hint-count derivation, kept out of the .svelte component so it is unit-testable.
+//
+// The badge shows the per-game hint allowance remaining plus the player's global hint
+// wallet. The server's hints_remaining folds the two together, but the wallet is global —
+// shared across every game — so caching the combined number per game makes it go stale the
+// moment a wallet hint is spent in another game. We therefore split it: the per-game
+// allowance is hints_remaining - wallet_balance (both from the same fetch, so it is stable
+// and cacheable), and the wallet is read live from the global profile, never the per-game
+// snapshot.
+
+import type { StateView } from './model';
+
+/**
+ * hintsLeft is the hint count for the badge: the per-game allowance remaining (the view's
+ * hints_remaining minus the wallet snapshot baked into that same view) plus the live global
+ * wallet balance. Passing the live wallet (not view.walletBalance) is what keeps the count
+ * correct when a wallet hint was spent in another game since this view was fetched.
+ */
+export function hintsLeft(
+  view: Pick<StateView, 'hintsRemaining' | 'walletBalance'> | null,
+  walletBalance: number,
+): number {
+  if (!view) return 0;
+  const allowance = Math.max(0, view.hintsRemaining - view.walletBalance);
+  return allowance + Math.max(0, walletBalance);
+}