Encrypted DNS (AdGuard Home, NextDNS, Quad9) with iCloud Private Relay

I host a AdGuard Home instance on a VPS for myself and family and I have it set up on my iPhone with a DoH profile. I cannot run a VPN all the time on my iPhone because of the extra battery drain. So I figured I’d give iCloud Private Relay another shot after 2 years and set it up. But then when I went to DNS Leak Test - BrowserLeaks to see the DNS entries, I could clearly see Akamai and Fastly, both of which Apple uses for iCloud Private Relay. Normally I see Cloudflare and Google as the DNS resolvers on this or any other DNS leak test website, but with Private Relay on, I am also seeing Akamai and Fastly. I also tried logging into my NextDNS account, setting it up on my iPhone with a DoH profile and testing again, but it was showing Akamai and Fastly along with the resolvers for NextDNS. Tried with Quad9’s profile as well.

According to this post from a year ago and according to Apple’s documentation, iCloud Private Relay should use the DNS I have specified with my encrypted DNS profile. What am I missing?

Consider using a separate device to handle the VPN like a router you can flash with OpenWRT or pfSense/OPNsense?