I was thinking about this yesterday when I ran a query and realized that I wouldn't actually know how to go about recreating my current search results.
Personally, I would much prefer some sort of automatic export to a third party service. Probably Dropbox and Google Drive would be the defaults for most person although if there were no restraints, an S3 compatible interface would be nice since I archive a bunch of stuff with Backblaze B2.
I'd say Raindrop.io's Dropbox and Google Drive automatic backups would be some prior art that comes to mind.