Huh. This seems like one of those "this must exist" situations, but I can't think of anything that does this, and a brief search suggests there may not be. The closest I could find was The Internet Archive's Archive-IT, though it's not an exact match. Otherwise, Archive Webpage , a pricey paid-for option (which seems like a terrible idea) appears to be the closest. OSS/self-host like Archivebox and Linkwarden don't really do this (though you can save/send a current tab to them), and apart from that... I don't really see anything.

The Firefox extension for archive.org has an option to archive the page you visit if said page hasn't been archived recently. Its not exactly what you're asking for, but similar

I think a squid proxy can do something like that, or could be tweaked to do that, if you really wanted to.

https://www.squid-cache.org/

Maybe offpunk could fit? I’ve never used it but I read the blog post about it

Check out archive warrior It’s dead simple to set up on Docker, and will run in the background while you help literally save the internet. Ignore the steps about watchtower, as that has been deprecated

There's a Firefox extension which makes a full-text index of every page you visit - it seems to work, but I found the search a bit unreliable so I stopped using it: https://addons.mozilla.org/en-US/firefox/addon/full-text-tabs-forever/

wget is the command line program to do what you're saying. Or what I use, anyway. Not tied to a browser, though. Maybe you could export your history and pipe it into wget if you're using Linux or have a Linux-like command line?

I also use the FF SingleFile plugin. Again, not automatic, though.

web pages used to sort of operate that way with the 'Temporary Internet Files' folder. i'm not sure how it's changed i just know this was how i used to circumvent websites that disabled right-clicking to save their images.