Every archiving tool out there makes trade-offs about what is archived and how. No one preserves the raw TLS encrypted H3 traffic because that's not useful. When you browse through an archiving MITM proxy, there are different trade-offs: there's an extra HTTP connection involved (that's not stored), a fake MITM cert, and a downgrade of H2/H3 connection to HTTP/1 (some sites serve different content via H2 vs HTTP/1.1, can detect differences, etc...)
The web is best-effort, and so is archiving the web.
The web is best-effort, and so is archiving the web.