These always just result in perpetual “I am not a robot” checking for me :/
Works for me in an incognito window for some reason. Oh, and you have to be on Chrome and not use Cloudflare DNS, I think
You don't need Chrome. Haven't touched it in half a decade and these work fine for me.
Might be a DNS over HTTPS issue. Try whitelisting archive.is if you're using Firefox (Firefox > Settings > Privacy & Security > [Scroll to bottom] "DNS over HTTPS" > "Manage Exceptions...") or turn off secure DNS in Chrome (Settings > Privacy and security > Security > Advanced section).
Rather than switching back to insecure DNS, you could just change to a DoH provider other than Cloudflare, since they're basically the only one that archive.is's operator is intentionally returning wrong results to.
Why would they intentionally return wrong results?