How can I add my AirPods to the Find My app?

See the following from Set up Find My on your iPhone, iPad, iPod touch, or Mac - Apple Support

How to add your AirPods, Apple Watch, or Beats product to Find My

If your AirPods, Apple Watch, or supported Beats product are paired with your iPhone, they're automatically set up when you turn on Find My iPhone.

To make sure you can find your devices even if they're powered off or disconnected, check that Find My network is turned on.

AirPods Pro or AirPods Max

1. Go to Settings > Bluetooth.
2. Tap the More Info button  next to your device in the list. 
3. Scroll down to Find My network. 
4. Make sure that Find My network is turned on.