“AirPods Pro 3 not in Find My on Mac: I have Airpods Pro 3 and Mac but not a iPhone. Airpods are connecting to the Mac but I cannot see them on my ‘Find My’ app. Is it a default thing or is there any issue with my Airpods? But when I connect my Airpods to other's iPhone, it is showing Airpods on ‘Find My’.”
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AirPods Not Showing Up on Paired Device:
AirPods are not assigned their own IP Address. As a result, they only show up in the location of the device these were last paired to. Being these are seen in Find My on your other devices, by not this Mac, that indicates that it is an issue pertaining to Find My in the Mac.
So, verify that you are connected to the Internet. Also, be on the same Apple ID. Turn off Find My and be certain Location Services is properly configured. It may be a firewall or VPN getting in the way here, as well , so turn both of those off.