You always make the claim with the carrier that brought you on the last flight to the final destination as shown on the ticket, regardless of which carrier is at fault.

Thus, you flew KE to TPE so you make the claim with KE and deal with KE. KE will deal with AC behind the scenes.

Once your bag arrives at TPE it should be delivered to you or available for pickup at the airport. If you have already left TPE they will be able to forward it to the nearest airport KE or an airline KE has an interline baggage agreement with flies to, likely with NZ, so likely anywhere in NZ that NZ flies to. Then you pickup the bag from there.