How to save selection as AUP file cluster

I have a imported a large WAV recording and I want to select regions and save them as individual audacity files for further editing.
I could cut the surrounding edges and “save as”, then reload for each region however this is slow. I just want to select a region and save it directly as an audacity AUP cluster.
I see a file: export-selection option and the drop down gives several formats however I don’t see an option to save it as an audacity aup file cluster.

Is there a way to do this?
Thank you,

I’d either use “Export Selected Audio” and export each selected part as a separate WAV file, or I’d label the parts that I want, then use “Export Multiple” and create a series of WAV files. I don’t see any advantage in saving them as Audacity projects as you can just as easily open Audacity and import one of the WAV files.
The "Export Multiple procedure is described here in the manual:

Thanks or the information. Makes sense