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.

gateway/internal/transcode/encode.go

@@ -223,6 +223,7 @@ func toWireState(s backendclient.StateResp) wire.StateView {
 		Rack:           s.Rack,
 		BagLen:         s.BagLen,
 		HintsRemaining: s.HintsRemaining,
+		WalletBalance:  s.WalletBalance,
 		Alphabet:       alphabet,
 	}
 }
@@ -278,6 +279,7 @@ func encodeHintResult(r backendclient.HintResultResp) []byte {
 	fb.HintResultStart(b)
 	fb.HintResultAddMove(b, move)
 	fb.HintResultAddHintsRemaining(b, int32(r.HintsRemaining))
+	fb.HintResultAddWalletBalance(b, int32(r.WalletBalance))
 	b.Finish(fb.HintResultEnd(b))
 	return b.FinishedBytes()
 }