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/inttest/game_test.go

@@ -424,13 +424,13 @@ func TestHintPolicy(t *testing.T) {
 		t.Fatalf("first hint: %v", err)
 	}
 	// The allowance is spent before the wallet: with an empty wallet, the state now reports no
-	// hints left and a zero wallet, so the per-game allowance (HintsRemaining-WalletBalance) is 0.
+	// per-game allowance left (HintsRemaining is the allowance alone; the wallet lives on the profile).
 	st, err := svc.GameState(ctx, g.ID, seats[0])
 	if err != nil {
 		t.Fatalf("state: %v", err)
 	}
-	if st.HintsRemaining != 0 || st.WalletBalance != 0 {
-		t.Errorf("after allowance hint: hints=%d wallet=%d, want 0/0", st.HintsRemaining, st.WalletBalance)
+	if st.HintsRemaining != 0 {
+		t.Errorf("after allowance hint: hints=%d, want 0", st.HintsRemaining)
 	}
 	if _, err := svc.Hint(ctx, g.ID, seats[0]); !errors.Is(err, game.ErrNoHintsLeft) {
 		t.Fatalf("second hint = %v, want ErrNoHintsLeft", err)
@@ -444,9 +444,10 @@ func TestHintPolicy(t *testing.T) {
 	if err != nil {
 		t.Fatalf("wallet hint: %v", err)
 	}
-	// The allowance stays exhausted; the wallet dropped 2->1, and WalletBalance carries it alone.
-	if res.HintsRemaining != 1 || res.WalletBalance != 1 {
-		t.Errorf("wallet hint: hints=%d wallet=%d, want 1/1", res.HintsRemaining, res.WalletBalance)
+	// The allowance stays exhausted (HintsRemaining is the allowance alone, so 0); the wallet dropped
+	// 2->1 and WalletBalance carries it (the client adopts it into the profile).
+	if res.HintsRemaining != 0 || res.WalletBalance != 1 {
+		t.Errorf("wallet hint: hints=%d wallet=%d, want 0/1", res.HintsRemaining, res.WalletBalance)
 	}
 	// game_players.hints_used counts BOTH hints (1 allowance + 1 wallet) — the per-game total
 	// that feeds the player's lifetime hint statistics, not just the allowance.