2016 Navigation unit plug and play?

From a quick glance at Toyota’s Repair Manual and Electrical Wiring Diagram, both available by subscription to techinfo.toyota.com, it looks like the connectors have the same shapes and use the same pinouts, so I don’t think any wires would have to be spliced. You should confirm this before proceeding, of course.

There is a more serious problem, however: the Navigation Receiver Assembly has an additional connector, not found on the (non-navigation) Radio & Display Receiver Assembly, for a GPS antenna mounted under the upper instrument panel, which is required for the navigation features to operate.

Toyota hasn’t updated their parts website to cover the Prius One, but from the application information in Figure 86-03 for the Prius Two, I believe the antenna (86860-78010 or 86860-0E070), bracket (86862-78010), and antenna cable (86101-47E10) may be present only on base-model (ZVW50) Prius cars sold with navigation systems in Mexico and South Korea, not on the Prius One or Prius Two sold here.

If my assumption is correct, and the GPS antenna and related parts are missing from your car, it’s likely that buying them, even at salvage prices, would cost more than a very nice aftermarket GPS navigation system.

(By the way, to receive SiriusXM satellite radio, the roof antenna assembly and its wiring harness would also have to be replaced, as I discussed in another thread.)