AirPod Hearing Aid setup w/o an iPhone or iPad

The usual setup is with an iPhone.

The iPhone for AirPods AND for commercial MFI Hearing Aids communicates with the hearing devices over Bluetooth for two things. It does both Control functions (Volume louder/softer and change to a different mode), and optionally forwards a sound stream (such as call audio or web streaming) if desired. Making that Bluetooth connection with commercial hearing devices requires that the hearing devices be Bluetooth-paired with the supervising device, typically an iPhone.

for AirPods, I honestly do not know whether your Apple-ID is a requirement to make that connection.

Only ONE such supervising device is accepted by most hearing devices, (I expect including AirPods), unless smart software is being used on the supervising device. This usually means that if paired with your iPhone for Control, you can not immediately accept "any old Bluetooth sound stream" from a nearby device

On the iPhone that uses:

Settings > accessibility > Hearing Devices > Mfi Hearing devices

That pane is not available on a Mac, at least not as recently as MacOS 15 Sequoia.

If you would like it to be added, you can make a Product Enhancement suggestion here:

Product Feedback - Apple

EDIT: that setting pane WAS added for MacOS 26 Tahoe, and described here:

Accessibility features for hearing on Mac - Apple Support

be sure to select MacOS 26 as you MacOS version for correct details.