On the buttons below the title, there should be an "archive" one for URL posts. It could use archive.is. The first time it's pressed an archive will be created, then automatically after that it'll go to the archived website. That's all done on their side as well.
You (Polsaker, I know you're reading this!) would just have to get the URL and then parse it into
javascript:void(open('https://archive.today/?run=1&url='+encodeURIComponent(POST URL HERE)))
Yes? No?
That'd be in the scope of YAPE rather than Phuks. We try not to rely on external APIs for site functionality