Entune Infotainment head unit does not boot up after replacing the battery?

That sounds like it will need to have the Entune software reloaded. There have been a few updates and service bulletins for the systems about it not booting and if the system locks up and generally the process is to reinstall the software updates through the dealer access system. There is no way to do it at home because the VIN has to be used on the network to be sure you get the correct software for the unit you have (two different makers of the hardware) In general on modern cars, battery replacement means you need a power supply to retain the systems as you change out the main battery. They will likely need to check the steering angle sensor and parking assist system as well. Disconnecting the battery causes those to switch to defaults that need to be adjusted to your vehicle.