No way that I know of, but it is a good idea. Supplemented by "search on sites I visited about a month ago", that should cover it.

Making that work across multiple devices is another can of worms. Possibly a very desirable can for some people, who'd like to host the data.

Self-hosting would imply some data syncing service, but it should be one where data is encrypted before leaving home (and stays encrypted until it returns to owner - not the case with Dropbox and most other services). Though the browser or browser extension could take care of that.