Extension request: WS→FCM fallback + chat-recovery on connect

Today the customer's "Perpanjang" only reaches the mitra via session-
scoped WS. If the mitra is on Home/Undangan, in a different session, or
backgrounded, the WS send no-ops and the 10s safeguard timeout fires
auto-reject (or auto-approve if the mitra happens to also have an
active general WS, depending on config) — either way the mitra never
saw the request.

Backend:
- extension.service.js::requestExtension now falls back to FCM via
  notification.service when the mitra isn't on the session WS. Mirrors
  the pairing notifyMitra pattern (Curhat Baru). Customer display name
  is pulled into the session lookup for the FCM body.
- shared.chat.routes.js: /chat/:sessionId/info now returns
  pending_extension (extension_id, duration_minutes, price,
  requested_at, expires_at, timeout_seconds) so the chat screen can
  rehydrate the accept/reject UI after a cold-start FCM tap. expires_at
  is derived from requested_at + extension_timeout_seconds config.

Mitra app:
- mitra_chat_notifier.dart::connect parses pending_extension from /info
  and seeds MitraChatConnectedData.extensionRequest — the existing
  _buildExtensionView renders unchanged.
- notification_service.dart::_navigateFromMessage handles
  type=extension_request → pushes /chat/session/<id>. Composes with
  the new /info pending_extension to bring the mitra straight into the
  accept/reject view.

Verified end-to-end on dev backend (FCM call returned sent=true; /info
returns pending_extension when within timeout window). Visual delivery
on emulator-5556 deferred — API 24 AVD queues FCM 5-30 min per
feedback-emulator-avd-versions.

Out of scope (follow-ups):
- Customer-side FCM for EXTENSION_RESPONSE (accepted/rejected/timeout)
- Perpanjang tab list endpoint + Flutter provider + UI

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

backend/src/routes/public/shared.chat.routes.js

@@ -56,7 +56,35 @@ export const sharedChatRoutes = async (app) => {
       return reply.code(404).send({ success: false, error: { code: 'NOT_FOUND', message: 'Session not found' } })
     }
     const goodbyeSubmittedByMe = await hasUserSubmittedClosure(sessionId, request.userType)
-    return reply.send({ success: true, data: { ...session, goodbye_submitted_by_me: goodbyeSubmittedByMe } })
+    // Surface any pending extension so the mitra chat screen can recover the
+    // _buildExtensionView state after a cold-start via FCM tap — without this,
+    // the WS EXTENSION_REQUEST frame fired earlier has nothing to bind to.
+    const [pendingExt] = await sql`
+      SELECT id, requested_duration_minutes, requested_price, requested_at
+      FROM session_extensions
+      WHERE session_id = ${sessionId} AND status = 'pending'
+      ORDER BY requested_at DESC
+      LIMIT 1
+    `
+    let pending_extension = null
+    if (pendingExt) {
+      const { getExtensionTimeoutConfig } = await import('../../services/config.service.js')
+      const { extension_timeout_seconds } = await getExtensionTimeoutConfig()
+      const requestedAtMs = new Date(pendingExt.requested_at).getTime()
+      const expiresAtMs = requestedAtMs + extension_timeout_seconds * 1000
+      pending_extension = {
+        extension_id: pendingExt.id,
+        duration_minutes: pendingExt.requested_duration_minutes,
+        price: pendingExt.requested_price,
+        requested_at: pendingExt.requested_at,
+        expires_at: new Date(expiresAtMs).toISOString(),
+        timeout_seconds: extension_timeout_seconds,
+      }
+    }
+    return reply.send({
+      success: true,
+      data: { ...session, goodbye_submitted_by_me: goodbyeSubmittedByMe, pending_extension },
+    })
   })
 
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