This seems like a lot of work just to make a pistol-caliber carbine that isn’t actually semi-auto. It is more of a double action, like a revolver; the action of pulling the trigger moves all the bits to cycle a new round. This would seem to make each trigger pull substantially more tiresome than for a conventional semi-auto carbine… more force needed, longer draw. The only obvious advantage would be that, being non-semi-auto, it just might play hell with various nutty local laws that foolishly ban semi-autos.
How the Providence Non Semi-Automatic Pistol Works, Shot Show 2019
One of the commenters over yonder says that this won’t be able to get around Californias laws, because California has written into law specifically what pistols are legal, not just which ones are illegal. My knowledge of California gun law is a little fuzzy, as I long ago put that blighted state in my rear view mirror.