Great question @F50 . The Chime Pros will not hand off connections with each other, as the initial setup establishes a secure connection to a specified Chime Pro. If you unplug the connected Chime Pro, the Video Doorbell will not connect to the other automatically.
Best practice with having multiple Chime Pros, is to keep the preferred one plugged in while setting up and connecting your Video Doorbell. Once your devices are online, and the Chime Pro is extending signal as intended, you'll be able to plug in the second Chime Pro without any network confusion. I hope this information is helpful!
Glad to see you were able to get these connected, and the signal extended. This is some great feedback, thank you for sharing in detail what your experience was like with this. I'll share it with the team, as I agree being able to select between Chime Pro networks in the app would make that process more efficient.