Apple - How to find the URLs accessed by iOS Apps?
You could use the Adblock app which is cheaper than Charles Proxy($2 vs $9) and is really easy to setup.
It has a local DNS proxy which can log all domains your device is connecting to and can also block domains or route them to different ones.
There is a wonderful app for that which I recommend (as a happy customer) and it’s called Charles Proxy.
You would install that on the iPhone and then connect to the proxy app as the VPN service which would then intercept all the calls and log them for you. This is far easier than paying for an external VPN and external DNS service and logging all the requests off the device. It also is much faster in my experience than offloading the inspection and logging to a remote computer.
I don’t leave the proxy on all the time, just when I need to see what’s happening, then I turn it off when I review the logs. I’m sure there are other options and look forward to other answers if there are better options than Charles Proxy.
If you have a network you control, look into a DNS service like pi-hole which can log all the lookups as well and make it easy to block ones you find objectionable.