What's the best way to fix this broken-wire to the 12V battery?

Go to a car extract the piece with a wire hanging out plug it to your business user red squeeze connector and you're done or could cross wind it solder it and shrink wrap it

 

It keeps the car from doing something I can't remember what right now charging sensing etc . They're a tool set that ll allow ya to remove the insert out of white plug Assy I have a key ring full of em

 

The small white wire senses the voltage right at the battery, so that the converter at the front of the car can regulate its output to accurately hit a voltage target at the battery.

If you look on this page, under Electrical Wiring Diagram, you will find two useful things:

• You'll learn about the Wire Harness Repair Manual, which is not paywalled. It doesn't have the latest precise information about your model and year, but it will answer your general questions about how to extract the old terminal from the housing, and how to make a proper and properly-protected parallel crimp repair to Toyota's standards.
• You'll learn about the Electrical Wiring Diagram for your car model, which will give you specific information like the Toyota part number for the proper repair terminal and for the parallel crimp sleeve to use with it. Scrolling down the page, you'll see your options for getting access to the EWD.

It's a little disappointing that most generic auto parts stores carry butt crimp splices instead of parallel ones. The ones you buy at a Toyota dealer are proper parallel splices, or you can get them from TE Connectivity.

When you go to a Toyota dealer to buy a "repair terminal" (using the part number you find in the EWD, or asking the parts-counter person to find it for you since they already have access), you get the proper terminal to click into that housing, preattached to a short length of wire so you can splice that to the good part of your car's existing wire.

If there is a salvage Prius near you where you can extract that terminal and cut its wire a few inches up to take it with you, that's essentially the same thing. It might be easier and cheaper than buying at the dealer, if you have convenient access to a nearby salvage Prius. If not, it could be more trouble than just going to the dealer.

 

It'll be ok; the converter just puts out a default reasonable voltage instead of tailoring it accurately to what the 12-volt battery needs.

I didn't remember whether a gen 2 will actually drive in that condition. Good to know that it only reports the error, and doesn't balk at driving.