How do I update firmware on AirPods

You don't need to update your AirPods; it happens automatically.

Apple explains this in the support document About firmware updates for AirPods which you seem to have been viewing prior to posting your question:

Firmware updates are delivered periodically while your AirPods are charging and in Bluetooth range of your iPhone; your iPad with iPadOS 16.1 or later; or your Mac with macOS Ventura.

Because firmware updates are delivered automatically, you don't need to update your AirPods.

The same document lists the current firmware number for these products:

Latest firmware versions

• AirPods Pro (2nd generation): 5A377
• AirPods Pro (1st generation): 4E71
• AirPods (2nd and 3rd generation): 4E71
• AirPods Max: 4E71
• AirPods (1st generation): 6.8.8

and if further shows that you can check the firmware version on yours by using your iPhone to navigate to Settings > Bluetooth, then tap the Info button  next to the name of your AirPods. Scroll down to the About section to find the firmware version.

The list at About firmware updates for AirPods - Apple Support

Latest firmware versions

• AirPods Pro (2nd generation): 5B58
• AirPods Pro (1st generation): 5B58
• AirPods (2nd and 3rd generation): 5B58
• AirPods Max: 5B58
• AirPods (1st generation): 6.8.8

So according to the list, my 2nd gen AirPods should be running 5B58 but it does not. I'm stuck at version 4E71. I got iPhone SE connected to AirPods sitting inside the charger (both are 100% charged). Left them alone for about 15 minutes. Nothing changed. Yes iPhone SE has internet access over WiFi.

Update

I checked my AirPods once again the next day. It does get updated to 5B58. Auto update works but very slow. My advice is stop staring at it. Just leave them in the charges and connected to your iPhone with internet access. It will eventually auto update.