Probably a little hacky but using a userscript & an archive tool could work. I have a userscript[1] that I've been using for years to archive some news sites but it just uses the Wayback Machine. It can probably be modified to wait more time and send the request to something like ArchiveBox[2] (or any archive tool that has a web interface). The downside is you'd need to whitelist specific sites (or whitelist everything and have a keybind or some content matching to activate the archive function? idk)

[1] https://gist.github.com/antiops/00a37a1de289415fa7cbd9b5d1d2...

[2] ArchiveBox, can have full text search: https://github.com/ArchiveBox/ArchiveBox