Post messages to a user's system tray using the extensions Notifications API. Start by declaring the "notifications" permission in the manifest.json.

{
  "name": "Drink Water Event Popup",
...
  "permissions": [
    "notifications",
  ],
...
}

Once the permission is declared, display a notification by calling notifications.create(). The following example is taken from the Drink water event popup sample. It uses an alarm to set a reminder to drink a glass of water. This code shows the triggering of the alarm. Follow the previous link to explore how this is set up.

chrome.alarms.onAlarm.addListener(() => {
  chrome.action.setBadgeText({ text: '' });
  chrome.notifications.create({
    type: 'basic',
    iconUrl: 'stay_hydrated.png',
    title: 'Time to Hydrate',
    message: "Everyday I'm Guzzlin'!",
    buttons: [{ title: 'Keep it Flowing.' }],
    priority: 0
  });
});

This code creates a notification on macOS like the following.