AirPods Pro 3 disconnecting from iMac Big Sur

I am on iMac (Retina 5K, 27-inch, Late 2014), Big Sur 11.7.10. I am trying to connect my new AirPods Pro 3.

I was successful in getting the AirPods to beep, a sound they seem to be generating.

I succeeded in getting a connection, in the Control Center they go blue, and in Settings > Bluetooth they show as Connected, but a few seconds later, or as soon as a sound source starts they disconnect. I reviewed:

If your AirPods or AirPods Pro won't connect

If your AirPods or AirPods Pro won't connect - Apple Support

How to reset your AirPods and AirPods Pro

How to reset your AirPods and AirPods Pro - Apple Support

…successfully stepping through the instructions, but still the same behavior. They connect, then disconnect. What else shall I try?

[Re-Titled by Moderator]

Original Title: AirPods Pro 3 disconnecting