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/transcode_test.go

@@ -59,7 +59,7 @@ func TestGameStateRoundTripForwardsUserID(t *testing.T) {
 		if r.URL.Path != "/api/v1/user/games/g-1/state" {
 			t.Errorf("unexpected path %q", r.URL.Path)
 		}
-		_, _ = w.Write([]byte(`{"game":{"id":"g-1","variant":"scrabble_en","status":"active","players":2,"to_move":1,"seats":[{"seat":0,"account_id":"u-7","score":5}]},"seat":0,"rack":[0,1],"bag_len":80,"hints_remaining":1}`))
+		_, _ = w.Write([]byte(`{"game":{"id":"g-1","variant":"scrabble_en","status":"active","players":2,"to_move":1,"seats":[{"seat":0,"account_id":"u-7","score":5}]},"seat":0,"rack":[0,1],"bag_len":80,"hints_remaining":4,"wallet_balance":3}`))
 	})
 	defer cleanup()
 
@@ -77,8 +77,8 @@ func TestGameStateRoundTripForwardsUserID(t *testing.T) {
 		t.Fatalf("handler: %v", err)
 	}
 	st := fb.GetRootAsStateView(payload, 0)
-	if st.BagLen() != 80 || st.RackLength() != 2 || st.HintsRemaining() != 1 {
-		t.Fatalf("state decoded wrong: bag=%d rack=%d hints=%d", st.BagLen(), st.RackLength(), st.HintsRemaining())
+	if st.BagLen() != 80 || st.RackLength() != 2 || st.HintsRemaining() != 4 || st.WalletBalance() != 3 {
+		t.Fatalf("state decoded wrong: bag=%d rack=%d hints=%d wallet=%d", st.BagLen(), st.RackLength(), st.HintsRemaining(), st.WalletBalance())
 	}
 	game := st.Game(nil)
 	if game == nil || string(game.Id()) != "g-1" || string(game.Variant()) != "scrabble_en" || game.ToMove() != 1 {
@@ -317,7 +317,7 @@ func TestHintRoundTrip(t *testing.T) {
 		if r.URL.Path != "/api/v1/user/games/g-3/hint" {
 			t.Errorf("unexpected path %q", r.URL.Path)
 		}
-		_, _ = w.Write([]byte(`{"move":{"player":0,"action":"play","words":["CAT"],"score":9},"hints_remaining":2}`))
+		_, _ = w.Write([]byte(`{"move":{"player":0,"action":"play","words":["CAT"],"score":9},"hints_remaining":2,"wallet_balance":1}`))
 	})
 	defer cleanup()
 
@@ -328,8 +328,8 @@ func TestHintRoundTrip(t *testing.T) {
 		t.Fatalf("handler: %v", err)
 	}
 	hr := fb.GetRootAsHintResult(payload, 0)
-	if hr.HintsRemaining() != 2 {
-		t.Errorf("hints remaining = %d, want 2", hr.HintsRemaining())
+	if hr.HintsRemaining() != 2 || hr.WalletBalance() != 1 {
+		t.Errorf("hint decoded wrong: hints=%d wallet=%d", hr.HintsRemaining(), hr.WalletBalance())
 	}
 	var move fb.MoveRecord
 	hr.Move(&move)