This, outside a browser, could be implemented as a server/client self-hosted solution with a back-end taking care of downloading/searching and an extension acting as client. Maybe it could even be made entirely as extension?
At the very least, it would need to be able to get the content pushed to it by the client, the way the client has it at moment of bookmarking, making the download/scraping kindof superflous.
Indexing and doing search, however, is hard, but solved. Hard in the sense that it is not something a firefox addon could do very well. I presume a (self)hosted meilisearch would suffice, though.
Edit: here's the description from their repo
"ArchiveBox is a powerful, self-hosted internet archiving solution to collect, save, and view sites you want to preserve offline.
You can set it up as a command-line tool, web app, and desktop app (alpha), on Linux, macOS, and Windows.
You can feed it URLs one at a time, or schedule regular imports from browser bookmarks or history, feeds like RSS, bookmark services like Pocket/Pinboard, and more. See input formats for a full list.
It saves snapshots of the URLs you feed it in several formats: HTML, PDF, PNG screenshots, WARC, and more out-of-the-box, with a wide variety of content extracted and preserved automatically (article text, audio/video, git repos, etc.). See output formats for a full list."