Seems to be some issues with existing VPN's and Private Relay. AdGuard ad-blocking (forget about the AdGuard VPN service for the time being) on iOS uses the VPN functions in the OS, so....are these two things going to conflict with each other?
appleinsider.com
How to turn off Private Relay in iOS 15 - and why you might want to | AppleInsider
Apple's forthcoming Private Relay feature in iOS 15 and macOS Monterey is a boon for privacy, but right now it won't always play nice with other VPNs. Here's what you can do about it.
appleinsider.com