This sequence resolved the removal problem for both my AirPods Pro 3 and my first-generation AirPods Pro:
1. Put the AirPods in your ears and connect them to your iPhone or iPad. They need to be connected for their settings to be available.
2. Open the AirPods' own settings, turn off Find My network, and check that it stays off.
3. Put both AirPods back in the case, close the lid, and wait 30 seconds.
4. In Bluetooth settings, select Forget This Device. Removing them through the Find My app had not worked for me.
5. Open the case and complete the factory reset using Apple's instructions for your model: How to reset your AirPods and AirPods Pro - Apple Support
I had already tried removing them through Find My and resetting them repeatedly. The sequence above finally worked for me.
Check for similarly named pairs. I had two pairs of AirPods Pro with similar names. I mistook the older pair's entry for the newer pair reappearing after removal. Both needed the same treatment.
This is what worked in my case. A reset alone, or seeing the generic "AirPods Pro" setup popup, does not prove the Apple Account association is cleared.
Related discussion describing a similar removal problem: How can I completely remove AirPods from … - Apple Community
