Zotero can sort of work like this. It's designed as a reference management tool but you can use it to save more or less any web page. It can also save actual

Zotero can sort of work like this. It's designed as a reference management tool but you can use it to save more or less any web page. It can also save actual snapshots of the page which makes it nice for "really saving" a page in case it disappears (although these days a lot of sites have junk that makes it not work that well). It is a little awkward having it as a separate app though.