Amazon has been progressively getting worse and worse. I was not a member of Prime for the video. It was a nice perk.
The combination of Amazon making it hard to search for things to buy, the huge amount of low quality crap for sale with confusing descriptions, and this most recent change of putting in place ads if I do not pay an additional fee has led me to cancel my subscription.
They have taken the enshittification too far. Good bye Amazon. Hello Home Depot, Target, et al.
The issue you are experiencing likely has nothing to do with the VPN. Network connectivity is not needed to unlock the car. I have been in places with no cell phone signal and it still works.
I do sometimes experience the same issue you are. If I wake up my phone, then it works. So it may be working for you not because you disabled the VPN, but because you woke up your phone and it then sent out the bluetooth signal to let the car know you were nearby.