"Private Relay uses both the CONNECT and CONNECT-UDP methods in HTTP/3 to set up connections quickly. For connections to websites that support TLS or QUIC, the initial TLS handshake messages are sent in the same set of data as the proxy request"

Would this not hinder the proposed mechanism discussed in the article?

Edit: forgive me, for my knowledge of networking is limited and I'd like to learn more if I am incorrect.

I fail to see how this is any different (for the purposes of getting around google) than any other VPN or proxy service out there. The proposed mechanism is just using a script that comes from the same server as the main website with perhaps slightly changed up code and a different file name to trick up adblockers. It can still fingerprint you without your actual ip address, as it collects data clientside.