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.

pkg/fbs/scrabble.fbs

@@ -240,6 +240,12 @@ table StateView {
   bag_len:int;
   hints_remaining:int;
   alphabet:[AlphabetEntry];
+  // wallet_balance is the requesting player's global hint-wallet balance, sent apart from
+  // hints_remaining (which folds the wallet in with the per-game allowance) so the client can
+  // separate the two: the per-game allowance remaining is hints_remaining - wallet_balance, and
+  // the wallet is a single global figure the client keeps live across games (added trailing —
+  // backward-compatible).
+  wallet_balance:int;
 }
 
 // GameActionRequest carries just a game id (pass / resign / hint / history).
@@ -290,10 +296,14 @@ table ComplaintRequest {
   note:string;
 }
 
-// HintResult is the top-ranked move plus the remaining hint budget.
+// HintResult is the top-ranked move plus the remaining hint budget. wallet_balance is the
+// global hint-wallet balance after spending (see StateView.wallet_balance), so the client
+// refreshes its live wallet and re-derives the per-game allowance (added trailing —
+// backward-compatible).
 table HintResult {
   move:MoveRecord;
   hints_remaining:int;
+  wallet_balance:int;
 }
 
 // DraftRequest saves the player's client-side composition for a game: a single

pkg/fbs/scrabblefb/HintResult.go

@@ -66,8 +66,20 @@ func (rcv *HintResult) MutateHintsRemaining(n int32) bool {
 	return rcv._tab.MutateInt32Slot(6, n)
 }
 
+func (rcv *HintResult) WalletBalance() int32 {
+	o := flatbuffers.UOffsetT(rcv._tab.Offset(8))
+	if o != 0 {
+		return rcv._tab.GetInt32(o + rcv._tab.Pos)
+	}
+	return 0
+}
+
+func (rcv *HintResult) MutateWalletBalance(n int32) bool {
+	return rcv._tab.MutateInt32Slot(8, n)
+}
+
 func HintResultStart(builder *flatbuffers.Builder) {
-	builder.StartObject(2)
+	builder.StartObject(3)
 }
 func HintResultAddMove(builder *flatbuffers.Builder, move flatbuffers.UOffsetT) {
 	builder.PrependUOffsetTSlot(0, flatbuffers.UOffsetT(move), 0)
@@ -75,6 +87,9 @@ func HintResultAddMove(builder *flatbuffers.Builder, move flatbuffers.UOffsetT)
 func HintResultAddHintsRemaining(builder *flatbuffers.Builder, hintsRemaining int32) {
 	builder.PrependInt32Slot(1, hintsRemaining, 0)
 }
+func HintResultAddWalletBalance(builder *flatbuffers.Builder, walletBalance int32) {
+	builder.PrependInt32Slot(2, walletBalance, 0)
+}
 func HintResultEnd(builder *flatbuffers.Builder) flatbuffers.UOffsetT {
 	return builder.EndObject()
 }

pkg/fbs/scrabblefb/StateView.go

@@ -144,8 +144,20 @@ func (rcv *StateView) AlphabetLength() int {
 	return 0
 }
 
+func (rcv *StateView) WalletBalance() int32 {
+	o := flatbuffers.UOffsetT(rcv._tab.Offset(16))
+	if o != 0 {
+		return rcv._tab.GetInt32(o + rcv._tab.Pos)
+	}
+	return 0
+}
+
+func (rcv *StateView) MutateWalletBalance(n int32) bool {
+	return rcv._tab.MutateInt32Slot(16, n)
+}
+
 func StateViewStart(builder *flatbuffers.Builder) {
-	builder.StartObject(6)
+	builder.StartObject(7)
 }
 func StateViewAddGame(builder *flatbuffers.Builder, game flatbuffers.UOffsetT) {
 	builder.PrependUOffsetTSlot(0, flatbuffers.UOffsetT(game), 0)
@@ -171,6 +183,9 @@ func StateViewAddAlphabet(builder *flatbuffers.Builder, alphabet flatbuffers.UOf
 func StateViewStartAlphabetVector(builder *flatbuffers.Builder, numElems int) flatbuffers.UOffsetT {
 	return builder.StartVector(4, numElems, 4)
 }
+func StateViewAddWalletBalance(builder *flatbuffers.Builder, walletBalance int32) {
+	builder.PrependInt32Slot(6, walletBalance, 0)
+}
 func StateViewEnd(builder *flatbuffers.Builder) flatbuffers.UOffsetT {
 	return builder.EndObject()
 }