fix(game): show granted/bought hints in-game — finish the D31 wire removal

The in-game hint badge ignored the payments hint wallet: loading a game clobbered
app.profile.hintBalance with the deprecated StateView.wallet_balance (zeroed in the
D31 domain removal but left in the protocol as a dead 0, then synced over the real
balance at game load).

Finish the removal honestly. StateView carries the per-game allowance alone
(hints_remaining); the purchasable wallet lives solely on the profile and the client
adds it (lib/hints). Removed StateView.wallet_balance across every layer — backend
StateView/DTO, notify.PlayerState (live events), gateway StateResp + wire.StateView,
the client model/codec/mock/localgame — and dropped the now-unused wallet arg from
hintsRemaining. The FBS field is tombstoned `(deprecated)` (not deleted) so the vtable
slots after it stay stable across a rolling deploy; no accessor is generated. HintResult
keeps wallet_balance (the real post-spend payments balance the client adopts into the
profile). The StateView type no longer has walletBalance, so the clobber cannot return
without a compile error.

Tests: hintsRemaining (2-arg); hints.hintsLeft (allowance + live wallet, no strip); the
game state/hint integration (allowance-only HintsRemaining); gateway transcode; FBS regen.

backend/internal/game/service.go

@@ -1207,7 +1207,7 @@ func (svc *Service) Hint(ctx context.Context, gameID, accountID uuid.UUID) (Hint
 		return HintResult{}, err
 	}
 	used++
-	return HintResult{Move: move, HintsRemaining: hintsRemaining(pre.HintsPerPlayer, used, walletAfter), WalletBalance: walletAfter}, nil
+	return HintResult{Move: move, HintsRemaining: hintsRemaining(pre.HintsPerPlayer, used), WalletBalance: walletAfter}, nil
 }
 
 // Candidates returns the to-move player's legal plays for a seated player on
@@ -1290,11 +1290,9 @@ func (svc *Service) GameState(ctx context.Context, gameID, accountID uuid.UUID)
 		Seat:   seat,
 		Rack:   g.Hand(seat),
 		BagLen: g.BagLen(),
-		// The hint wallet moved to payments (svc.hintWallet); the deprecated accounts.hint_balance
-		// is no longer read, so the wire wallet is 0 and HintsRemaining is the per-seat allowance.
-		// The client adds the profile's payments hint balance on top (lib/hints.hintsLeft).
-		HintsRemaining: hintsRemaining(pre.HintsPerPlayer, pre.Seats[seat].HintsUsed, 0),
-		WalletBalance:  0,
+		// HintsRemaining is the per-seat allowance only; the purchasable wallet lives on the profile
+		// (payments) and the client adds it (lib/hints.hintsLeft).
+		HintsRemaining: hintsRemaining(pre.HintsPerPlayer, pre.Seats[seat].HintsUsed),
 		// vs_ai idle-hint gate (seconds left; 0 for a human game / first move / not your turn).
 		HintUnlockLeftSeconds: hintUnlockLeftSeconds(pre, seat, svc.clock()),
 	}, nil
@@ -1775,10 +1773,10 @@ func (svc *Service) DictBytes(variant engine.Variant, version string) ([]byte, e
 	return svc.registry.DictBytes(variant, version)
 }
 
-// hintsRemaining is a player's remaining hint budget: the unspent per-game
-// allowance plus the profile wallet.
-func hintsRemaining(allowance, used, wallet int) int {
-	return max(0, allowance-used) + wallet
+// hintsRemaining is the unspent per-game hint allowance. The purchasable wallet is separate,
+// carried on the profile (payments), and the client adds it (lib/hints.hintsLeft).
+func hintsRemaining(allowance, used int) int {
+	return max(0, allowance-used)
 }
 
 // allowedTimeout reports whether d is one of the offered move clocks.