2 error codes left on my 2016

“Permanent” doesn’t mean forever, just that the electronic control unit (ECU) involved will clear the diagnostic trouble code (DTC) only after it observes enough driving without detecting the problem again. The SAE J1979 standard explains: “The intended use is [...] to prevent vehicles from passing an in-use inspection simply by disconnecting the battery or clearing DTCs with a scan tool prior to the inspection.”

Indeed. The Repair Manual (more info) says that SAE DTC U0284 is equivalent to Toyota DTC U028487, Lost Communication with Active Grille Air Shutter Module “A” Missing Message, which indicates a loss of CAN bus communication between the engine control module (ECM) and the swing grille actuator assembly.

SAE DTC P0562 is equivalent to Toyota DTC P056014, System Voltage Circuit Short to Ground or Open, indicating a problem with the ECM power supply, which could easily be explained by the missing fuse.

If the underlying trouble is gone, I’d expect both DTCs to be cleared on their own after several drive cycles.

From the coverage chart (PDF), it seems this device may not be able to retrieve DTCs related to the hybrid system, even from Prius models that predate its software. The fact that it’s displaying SAE and not Toyota DTCs also suggests that it may not be useful for diagnosing actual malfunctions unrelated to the engine and its emission controls. I’d suggest a Toyota Techstream diagnostic system instead.