2016 Prius door lock issues

For the fuel door... have you tried pulling the hidden lever?

The manual says:

When the fuel filler door cannot be opened by pressing the inside switch:

1 Open the back door and remove the cover underneath the luggage compartment light.

2 Pull the lever backward and check that the fuel lid opens.

If that works, then the mechanics are working at least... and somebody else might be able to help with the electronic side.

 

For the fuel lid, I’d suggest the thirteen-step diagnostic procedure in the Repair Manual (available by subscription to techinfo.toyota.com), under Vehicle Exterior: Door/Hatch: Fuel Lid Opener System: Fuel Lid Opener Does Not Operate. You’d need a Toyota Techstream diagnostic system to do some of the steps, but you could inspect the fuel lid lock with motor assembly, fuel lid opener switch, harnesses, and connectors with just a digital multimeter and the tools needed to remove and install the relevant parts.

Similarly, for the power door locks, I’d suggest starting at Vehicle Interior: Door Lock: Power Door Lock Control System: Problem Symptoms Table.

The text and illustrations from the Repair Manual are also available in the ChiltonLibrary service, to which your local public library sponsors free access. (Click “Automotive Repair” on that page.) The contents are organized a bit differently there; select 2016 Toyota Prius, and then click Repair > Body > Exterior > Door/Hatch > Fuel Lid Opener System or Repair > Body > Interior > Power Door Lock Control System to see the topics I mentioned above.

 

Of the suggested solutions price too demanding of your personal resources, perhaps your warranty will enable a free dealer performed repair.