AirPods to connect to Apple Watch ONLY

I am a proud owner of a new Apple Watch Ultra. This model appears to be able to accomplish what I’d been hoping for since the original Apple Watch was released: to be my primary mobile device to last me all day. This was never possible with the previous generations of Apple Watch because they simply didn’t have the battery capacity to endure strenuous use all day. But the Ultra has that ability. I hate having to tote my iPhone around and, with the cellular function and battery capacity of the Ultra, I don’t have to. I can stream my entire iTunes Match library through the Ultra wherever I am—I can go out walking the dog, walk around the office, walk around home—and enjoy the music playing through my AirPods Pro without interruption.

Well, almost.

The issue is that, given the opportunity, the AirPods Pro still prefer to connect to my iPhone if it’s in range, even with the Bluetooth settings set to “When last connected to this iPhone”.

Scenario:

I’m listening to music coming from the Ultra and I’m happy. I then stop the music for a short while because I need to talk to someone. I then squeeze the stem of the AirPods Pro to resume playback, but now the playback is coming from the iPhone. Totally different song. During that moment when the Ultra was paused, the AirPods Pro decided to switch back to the iPhone. This is what I want to prevent. I want the AirPods to prefer my Ultra over all devices.

Currently, if I choose “Forget Device” on the iPhone so it forgets about the AirPods Pro, then the Ultra forgets it, too.

Anyone know a way to only have a Watch aware of Bluetooth earphones without the iPhone also knowing?