Maybe take the broken CO2 cartridge, add some super glue to the end, screw it back in and - after letting it dry for some hours - try to screw the entire bottle out again.

Alternatively, if you can reach the broken part with a dremel, you could try to make a small cut into it (brass is pretty soft) and use a flat screwdriver in that cut to screw it out.

If successful, please don’t exchange the broken cartridge the regular way but send a mail to the manufacturer to get it exchanged. Otherwise the broken one might find its way into the next unlucky household.