我没有找到任何正确的解决方案来实现推送通知与WebSocket。
我的简单要求，如WhatsApp聊天，当消息到来时，它以推送通知的形式显示消息。
Here is the documentation用于推送通知。

/**
 *  Push notification code
*/

import { PushNotifications } from '@capacitor/push-notifications';

const addListeners = async () => {
  await PushNotifications.addListener('registration', token => {
    console.info('Registration token: ', token.value);
  });

  await PushNotifications.addListener('registrationError', err => {
    console.error('Registration error: ', err.error);
  });

  await PushNotifications.addListener('pushNotificationReceived', notification => {
    console.log('Push notification received: ', notification);
  });

  await PushNotifications.addListener('pushNotificationActionPerformed', notification => {
    console.log('Push notification action performed', notification.actionId, notification.inputValue);
  });
}

const registerNotifications = async () => {
  let permStatus = await PushNotifications.checkPermissions();

  if (permStatus.receive === 'prompt') {
    permStatus = await PushNotifications.requestPermissions();
  }

  if (permStatus.receive !== 'granted') {
    throw new Error('User denied permissions!');
  }

  await PushNotifications.register();
}

const getDeliveredNotifications = async () => {
  const notificationList = await PushNotifications.getDeliveredNotifications();
  console.log('delivered notifications', notificationList);

/**
   Web Socket related code
*/

// Create WebSocket connection.
const socket = new WebSocket("ws://localhost:8080");

// Connection opened
socket.addEventListener("open", (event) => {
  socket.send("Hello Server!");
});

// Listen for messages
socket.addEventListener("message", (event) => {
  console.log("Message from server ", event.data);
  PushNotifications.send("Message from server ", event.data);  // added for testing but does not work
});

}