feat(approvals): gate push Approve/Deny buttons on the opt-in setting too

One switch now governs the whole feature: with approvalsInboxEnabled off
(the default), sendPushNotifications strips the actions and approvalId
from permission push payloads, so the buttons no longer render at all
(pre-inbox they rendered and did nothing). The page-side action relay is
gated the same way for stale notifications sent before the toggle
flipped. Only the store and answer endpoints keep running, so enabling
the toggle surfaces anything already pending immediately.

sendPushNotifications is async now (cached settings read); all call
sites were already fire-and-forget. Covered by three new payload tests
alongside the existing hostTitle suite.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

test/push-payload-host-title.test.ts

@@ -76,11 +76,11 @@ describe('push payload hostTitle (Web Push hostname plumbing)', () => {
     setVapidDetails.mockClear();
   });
 
-  it('includes hostTitle = codeman:<titleHostname> in the payload', () => {
+  it('includes hostTitle = codeman:<titleHostname> in the payload', async () => {
     const server = makeServerWithHost('laptop');
-    (
+    await (
       server as unknown as {
-        sendPushNotifications: (e: string, d: Record<string, unknown>) => void;
+        sendPushNotifications: (e: string, d: Record<string, unknown>) => Promise<void>;
       }
     ).sendPushNotifications('hook:idle_prompt', {
       sessionId: 's-1',
@@ -93,11 +93,11 @@ describe('push payload hostTitle (Web Push hostname plumbing)', () => {
     expect(payload.title).toBe('Waiting for Input');
   });
 
-  it('falls back to os.hostname() when --title-hostname is not provided', () => {
+  it('falls back to os.hostname() when --title-hostname is not provided', async () => {
     const server = makeServerWithHost(''); // empty -> constructor uses getHostname()
-    (
+    await (
       server as unknown as {
-        sendPushNotifications: (e: string, d: Record<string, unknown>) => void;
+        sendPushNotifications: (e: string, d: Record<string, unknown>) => Promise<void>;
       }
     ).sendPushNotifications('hook:permission_prompt', {
       sessionId: 's-2',
@@ -111,18 +111,18 @@ describe('push payload hostTitle (Web Push hostname plumbing)', () => {
     expect(payload.title).toBe('Permission Required');
   });
 
-  it('different WebServer instances ship distinct hostTitles', () => {
+  it('different WebServer instances ship distinct hostTitles', async () => {
     const a = makeServerWithHost('host-a');
     const b = makeServerWithHost('host-b');
 
-    (
+    await (
       a as unknown as {
-        sendPushNotifications: (e: string, d: Record<string, unknown>) => void;
+        sendPushNotifications: (e: string, d: Record<string, unknown>) => Promise<void>;
       }
     ).sendPushNotifications('hook:stop', { sessionId: 's-a', sessionName: 'A' });
-    (
+    await (
       b as unknown as {
-        sendPushNotifications: (e: string, d: Record<string, unknown>) => void;
+        sendPushNotifications: (e: string, d: Record<string, unknown>) => Promise<void>;
       }
     ).sendPushNotifications('hook:stop', { sessionId: 's-b', sessionName: 'B' });
 
@@ -164,3 +164,66 @@ describe('service worker displayTitle composition (mirrors sw.js)', () => {
     expect(computeSwDisplayTitle({})).toBe('Codeman');
   });
 });
+
+// ─── Approvals Inbox gating ──────────────────────────────────────────────
+// The Approve/Deny action buttons answer through the Approvals Inbox, so the
+// payload ships them (and the approvalId they act on) only when the OPT-IN
+// `approvalsInboxEnabled` setting is on. Pre-inbox these buttons rendered and
+// did nothing; with the feature off they must not render at all.
+
+interface ApprovalAwarePayload extends PushPayload {
+  approvalId?: string;
+}
+
+function setSettings(server: WebServer, settings: Record<string, unknown>): void {
+  (server as unknown as { readSettings: () => Promise<Record<string, unknown>> }).readSettings = async () => settings;
+}
+
+async function sendPermissionPush(server: WebServer): Promise<ApprovalAwarePayload> {
+  await (
+    server as unknown as {
+      sendPushNotifications: (e: string, d: Record<string, unknown>) => Promise<void>;
+    }
+  ).sendPushNotifications('hook:permission_prompt', {
+    sessionId: 's-gate',
+    sessionName: 'sess',
+    tool_name: 'Bash',
+    approvalId: 's-gate:1',
+  });
+  return lastPayload() as ApprovalAwarePayload;
+}
+
+describe('push payload Approvals Inbox gating', () => {
+  beforeEach(() => {
+    sendNotification.mockClear();
+  });
+
+  it('strips actions and approvalId when the setting is off (the default)', async () => {
+    const server = makeServerWithHost('gate-off');
+    setSettings(server, {});
+    const payload = await sendPermissionPush(server);
+    expect(payload.actions).toBeUndefined();
+    expect(payload.approvalId).toBeUndefined();
+    // The notification itself still goes out; only the inbox parts are gated.
+    expect(payload.title).toBe('Permission Required');
+  });
+
+  it('ships Approve/Deny actions and the approvalId when the setting is on', async () => {
+    const server = makeServerWithHost('gate-on');
+    setSettings(server, { approvalsInboxEnabled: true });
+    const payload = await sendPermissionPush(server);
+    expect(payload.actions).toEqual([
+      { action: 'approve', title: 'Approve' },
+      { action: 'deny', title: 'Deny' },
+    ]);
+    expect(payload.approvalId).toBe('s-gate:1');
+  });
+
+  it('an explicit false behaves like the default (only true enables)', async () => {
+    const server = makeServerWithHost('gate-false');
+    setSettings(server, { approvalsInboxEnabled: false });
+    const payload = await sendPermissionPush(server);
+    expect(payload.actions).toBeUndefined();
+    expect(payload.approvalId).toBeUndefined();
+  });
+});