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?
Please, no. They render websites terribly and the performance is horrible. Also they block me from accessing archive.li archived pages because they're butthurt the registrar forbid them to have illegal content on their website.
When you need something archived, use archive.org.