Why Does My Apple Watch Lose Connection to My iPhone When Using a VPN
I have come to the conclusion that a VPN simply causes a lot of connection issues when dealing with iOS and watchOS. For example, I found that iMessage and standard texts were not working correctly on my iPhone when my VPN was on. This is all besides the Apple Watch connection issues.

My answer is a non-answer in that VPNs and iOS/WatchOS do not play well together. I wish I could point you towards some documentation on why, but I cannot find any.