I use NetNewsWire. Since I am happily entrenched in the Apple ecosystem, it works great with its iCloud syncing. This way I can use it on my phone and laptop while not having to set up any server-side infrastructure or rely on a third party to host anything. (Granted I am relying on the iCloud storage for device syncing. But it did not involve any kind of setup and the files are encrypted such that Apple cannot read them.)

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.