Bluetooth headset only works when System Settings->Sound->Input tab is open
I have a 2019 Macbook Pro on Sonoma 14.0. A week or so ago my generic bluetooth headset quit working - no sound, no mic input. I can't hear sound from any programs or apps, and no-one can hear me. The headset shows as connected on my mac. The headset still works perfectly with my work 2021 M1 Macbook Pro.
I am not on mute, and both my headphone volume and program / app volume are up.
By accident I discovered that when I go to System Settings-> Sound -> Input, I can hear sound out of my bluetooth headset again. It works perfectly when Input is open, and I can hear sound from all programs and apps. When I navigate away from this screen the sound stops working again after a second or so.
I don't see anything that looks like error messages in Console.
How can I get my bluetooth headset to work again without keeping the Sound Input tab open?
Mac Pro (2019)