I ran into this same problem after updating iOS to 15.4.1. VPN was not the issue.
I was able to work around the problem by doing the following:
Settings -> Wifi -> i (next to the network name) -> Configure DNS -> Manual
* Then removed my router's ip (192.168.0.1 in my case)
* Added Google's DNS server (8.8.8.8)
Before someone suggests that my router is misconfigured... my other devices (such as my MBP) respond perfectly to DNS requests directed at my router and this problem only occurred on my iPhone after I updated iOS. It may be related to an incompatibility w/ my router's DNS w/ the latest iOS update, not sure. I have a NetGear Nighthawk R8000P w/ firmware V1.4.3.88_1.3.50.
Also... you may want to plug in your isp's DNS server(s) rather than 8.8.8.8 which I just used for testing.