The data on the card inserted into the camera transfers files to the aircraft.
I strongly suggest using the “manual” SD card update method. The only things to remember is to not unzip the files before installing them on the card, make sure the card is completely empty before placing files on the card, load only one file at a time on the card, either ST-16 or camera/aircraft, never both simultaneously, and clear the card of all files after each device has been updated before doing the second device.
One handy tip that always works when searching for newly installed files to bind to, place the ST-16 in Team mode instead of tipping the H to enter bind mode. Do this before going to settings to search for the new firmware. Team mode puts the H in binding mode automatically.