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LocalSend - Share files to nearby devices
(localsend.org)
This is a most excellent place for technology news and articles.
I kid you not, I was actually looking for a solution like that yesterday! hopefully it'll handle a few tens of gigabytes between my two Linux laptops.
This is one file at a time. It's designed more for very quick "Oops I need that photo" sort of stuff.
What you want to do is better served by NFS, SMB or SFTP.
It does actually support several files, folders, or anything.