Save a SCENE as a new, different *.blend file? / extract or export an individual Scene?

Is there a function that saves an individual Scene as a new *.blend file?

I often want to do this.

(Fancy optional version: save ALL the Scenes in a given *.blend file as separate files. But that’s not really what I need.)

Reverse option is to open new file in Blender and append desired scene from actual blend-file.

Both would be useful.