Re-starts by itself. Won't start. Loses 12V battery power?

There is no alternator in a Prius. There is a DC to DC converter that is located inside the inverter assembly. It converts the high voltage supplied by the hybrid battery, when the car is in Ready, down to low voltage (14.1v to ~ 13.2v) for the 12v system in the car.

 

Oh, that tester. I have one. That Ah rating is complete BS. The little electronic testers have no way to calculate that value accurately. See:

Are Battery Conductance Testers Worth It? - Marine How To

That Viking had some other bug, which I'm trying to remember. I think maybe it was that if the expected Ah was set to a different value, like 60 instead of 45, the measured Ah would change. Which of course makes no sense at all. It reads voltage well enough and may be ballpark for CCA and resistance (although in that link an earlier Centech tester was way off for CCA). If you really want to measure battery capacity the gold standard is a C/20 discharge for 20 hours using a device like a DTL150 to lock the current (and set safe lower limits for the voltage). And you have to log voltage vs. time to see if there is anything really funky going on. Otherwise the device can tell you how many Ah drained before it hit the low end cutoff condition. Except don't, because fully discharging an AGM isn't good for it, and don't try to discharge at a higher current for less time because Peukert's law kicks in and the measurable capacity actually changes. For the battery currently in the car I did C/20 for 2 hours (taking datapoints, to form a baseline measurment) and will compare that with similar measurements when needed later.

All that said, the voltage is OK and as long as it doesn't totally collapse when the car tries to start the battery isn't the problem. A DVM isn't good at showing that because they take too long to update the voltage. If you can get your hands on an old analog voltmeter it can follow the voltage well enough to see if it drops down to 10.5V or less. These are still available and one can be had for less than $20, which is roughly the price of this one (never used that particular model, just an example)

Gardner Bender GMT-318 Analog Multimeter, 6 Funct, 14 Range, Tests AC/DC Volt, DC Current, Resistance, Decibel, and Battery, Manual Range, 1/Ea