If I wanted to take advantage of the new Picade X on my old original Picade, am I right in thinking that I would need to purchase the Picade X Hat, the new wiring loom, and I think I would need the same joystick that the new Picade uses due to the wiring loom being different, and the connectors on the hat and joystick being different.
This is correct- yes! You can pick them all up here- https://shop.pimoroni.com/products/joystick
A little creative wiring might eliminate the need to replace your joystick since the electrical connections are still fundamentally the same.
You’d also be best served by creating a new RetroPie image from the latest download, and moving your ROMs/configuration across since you’ll need updated software to support Picade X HAT and in-place upgrades can be tricky!
If you careful, you can often remove and swap pins around in connectors with a pin or needle. Look for a locking tab on one side of the connector shell. Carefully lift that slightly and you can pull the wire out of the shell. Then put it in the position “you” want. Might save you from having to buy a new joystick. Just be careful, lift the tab too much and it can break off, or not go back to the lock position. Even if that happens, there should be enough friction that the wire won’t come loos on its own once plugged into the joystick. It just makes plugging it in tricky.