I know that since I upgraded my ps4 internal hdd a few years ago, Sony have done something with the harddrives plugged into ps4 on usb wires, but I am unsure what exactly. I don't think you can install games to and run games off the external hdds, can you? I think its more like a backup solution so you didn't have to re-download games from pstore? Brother is interested in this external hdd:
https://www.amazon.co.uk/gp/product/B00TKFEE5S/
https://www.amazon.co.uk/gp/product/B00TKFEE5S/