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/backendclient/api.go

@@ -162,6 +162,7 @@ type StateResp struct {
 	Rack           []int               `json:"rack"`
 	BagLen         int                 `json:"bag_len"`
 	HintsRemaining int                 `json:"hints_remaining"`
+	WalletBalance  int                 `json:"wallet_balance"`
 	Alphabet       []AlphabetEntryJSON `json:"alphabet,omitempty"`
 }
 
@@ -331,6 +332,7 @@ func (c *Client) ChatPost(ctx context.Context, userID, gameID, body, clientIP st
 type HintResultResp struct {
 	Move           MoveRecordResp `json:"move"`
 	HintsRemaining int            `json:"hints_remaining"`
+	WalletBalance  int            `json:"wallet_balance"`
 }
 
 // EvalResultResp is an unlimited move preview. Dir is the orientation the backend