The steam dock, and many other docks, just takes power from it’s usb-c power-in socket. It doesn’t care if the power comes from the AC adapter it comes with, or any other usb-c pd power source.
So, enter “12v USB-C PD 45w” into google and you will find a plethora of cigarette socket usb-c pd adapters that you can power docks with.
There is no such thing as a fake/counterfeit steam deck. There is, however, such a thing as saying you have a steam deck for sale when you actually don’t, so being able to see it IRL and confirming it looks like a steam deck is enough (preferably turning it on too)