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.

backend/internal/game/service.go

@@ -1042,7 +1042,7 @@ func (svc *Service) Hint(ctx context.Context, gameID, accountID uuid.UUID) (Hint
 		}
 		walletAfter--
 	}
-	return HintResult{Move: move, HintsRemaining: hintsRemaining(pre.HintsPerPlayer, used, walletAfter)}, nil
+	return HintResult{Move: move, HintsRemaining: hintsRemaining(pre.HintsPerPlayer, used, walletAfter), WalletBalance: walletAfter}, nil
 }
 
 // Candidates returns the to-move player's legal plays for a seated player on
@@ -1130,6 +1130,7 @@ func (svc *Service) GameState(ctx context.Context, gameID, accountID uuid.UUID)
 		Rack:           g.Hand(seat),
 		BagLen:         g.BagLen(),
 		HintsRemaining: hintsRemaining(pre.HintsPerPlayer, pre.Seats[seat].HintsUsed, acc.HintBalance),
+		WalletBalance:  acc.HintBalance,
 	}, nil
 }