I think a chassis is the deciding factor, since you can shove modern components in 50+ year old chassis and build street legal hotrods. You register it as that old chassis model from whatever manufacturer built it.

As I understand BYD use less components than the other traditional car manufacturers (more brains/integration in axle vs having lots of CAN connected shit around the car) so in theory I could see builders installing a BYD drivetrain into an old chassis the same way people can do LS swaps into Miatas.