Is there a feature of DNS I'm unaware of, that queries more than just the domain part? https://example.com?token=<secret> should only lead to a DNS query with "example.com".
The problem isn't DNS in GP. DNS will happily supply the IP address for a CDN. The HTTP[S] request will thereafter be sent by the caller to the CDN (in the case of CloudFlare, Akamai, etc.) where it will be handled and potentially logged before the result is retrieved from the cache or the configured origin (i.e. backing server).
Correct, DNS only queries the hostname portion of the URL.
Maybe my attempt to be thorough – by making note of DNS along side HTTP since it's part of the browser ↔ network ↔ server request diagram – was too thorough.