Cloudflare is one of the operators of egress nodes for iCloud Private Relay, along with Akamai and Fastly and maybe some others (IIRC). So you probably have issues with Archive.is when you're connected through Cloudflare. Although I'm not sure how DNS resolution works on private relay (since it's the DNS server rather than the egress proxy that causes the issue - but if the egress proxy is making the DNS requests then that would explain it).