I am trying to take notes while out walking and listening to a podcast. My watch dictation works fine without AirPods but does not work with AirPods. Anything I can do?
Might be worth a read of this thread if you haven’t already. Not solutions, just an indication that it is not necessarily in the full control of the developer what microphone the OS picks. 
But it is worth testing what happens with the different dictation options.
There is a problem with the program, though. I’m experiencing this on my MacBook Pro. I’ve got the latest version of Drafts installed and can’t dictate using my AirPods 2nd Gen. My AirPods Pro work fine, as do my other wired headsets.
When I try to start the dictation I receive the error “Unable to start audio capture.” and “Unable to start dication. Check that Drafts has permissions to use both the microphone and speech recognition in System Preferences > Security & Privacy.”
I have already made sure Drafts has proper permissions and still receive this error when using the AirPods 2nd Gen.