So this would take the IIIF Manifest JSON URL, in your example:
https://iiif.lib.harvard.edu/manifests/drs:4787716
and upload all the files there to Commons?

Would it require an intermediate step, like a preview of all the images, with checkboxes, etc., or would a full upload of everything be sufficient?

In T358224#11542808, @Magnus wrote:

So this would take the IIIF Manifest JSON URL, in your example:
https://iiif.lib.harvard.edu/manifests/drs:4787716
and upload all the files there to Commons?

Yes; with any included metadata applied as titles, descriptions, dates etc.

Would it require an intermediate step, like a preview of all the images, with checkboxes, etc., or would a full upload of everything be sufficient?

I suppose a full upload might work, but I envisaged a page like that offered by your Flickr2Commons tool where the user could exclude images (some might be non-free, for instance), rename them, edit descriptions, add categories, and so on.