Inverter Pump / 12v battery issues

Hello Prius friends!

My 2007 Prius’ inverter water pump failed about 2 months ago and my friend’s dad mistakenly diagnosed it as a bad 12v battery and replaced that. A couple weeks later, I had the codes read and discovered it was actually the inverter water pump that was failing and had that replaced (Professionally this time!) After driving fine for a couple weeks, I tried to turn the car on one morning and the battery was dead. I jumped and charged it and now the voltage is reading ~11.6v with headlights off and ~10.6v with headlights on. The car is not showing any codes!

Clearly I need a new battery but I’m wondering if it is possible that my inverter is failing? Or if driving with the failing inverter water pump for a couple weeks killed my brand new battery… Is there a way to see if the inverter is bad?

Thanks!!!