GDPR does in fact apply to publicly available information though, as their definition for personal data is “any information relating to an identified or identifiable person” while making personal data available is likely beyond just indexing and there are likely other laws that cover that, though by doing so you would still have to index and store said data, so Article 17 would apply in most cases.
Given that the web page has enough traffic they will archive it, heck, check your privacyguides account, they might have already archived that, and if they haven’t, they will one day. That is the point I’m trying to say, is that the Internet Archive archives random people’s stuff that might contain personal information instead of just the things that have actual historical value.