Under hood battery at this point is probably dead since charging system is not working . You will need to replace that battery and put the car on a charger for trouble shooting. You may want to find a different shop to work on it. It seems they ordered everything without actually troubleshooting it, getting codes and following the troubleshooting processes from the Factory Service Manual.
There are two ways to troubleshoot: One is to carefully read codes, follow processes and narrow down to the one failed part. The other is just throw parts at it randomly. The second is what this dealer is doing. Find a more knowledgeable dealer who is very familiar with CR-Zs and is ASE certified. Talk to the service manager, if you keep it at the same dealership and ask if they can put their most knowledgeable person on it who knows CR-Zs specifically. Ask if their dealership is familiar with CR-Zs and if they are not can they recommend another shop that is, whether that shop is a Honda dealer or independent specialist.
I hope when all the right processes are followed you will be able to put your CR-Z back on the road.