Are your AirPods paired with your watch ?
If so you could try turning your watch off to see if that changes the microphone connectivity on a call.
You may also want to try calling yourself from a landline to see if its really your issue or just someone else's.
Ive tried it with both versions of AirPods as well as IOS 13-13.1.2 xS and now 11 Pro (series 4 watch os 6-6.1) and haven't been able to reproduce the issue.
No you cannot rearrange bluetooth devices however when all devices are forgotten the one you pair first becomes first.
I had a stack full of Tiles (trackers) for testing and my bluetooth earpieces and headsets at the bottom were always the last to connect. Added 10ns of seconds to call connect, if at all
Best of luck.