Odd 12v battery question MY23 PS2

So, I am returning my 23PS2 lease early because I hit the mileage mark. I purchased another PS2 from another dealership and it's getting delivered soon. I haven't driven it in a couple of weeks but the other day I decided to drive it and of course the 12v was dead. Ok no problem, I jump started it and all was good so I thought. Later on that day, I went to start the car because based on what I read the 12v would charge from the main battery if it was plugged in the wall. Of course it didn't start and the car was completely dead. Like nothing came on, no interior lights....nothing, I went and placed the volt meter on the terminals and it showed 0v. I thought that didn't make sense how could a 12v show 0v. Once again, I jump charged it last night and it came to life. Now to make matters worse I am getting it inspected tomorrow for the return to the dealership.

Now here is where it's a little odd, this am I went to get something out of the car and the car screens lit up like normal. I didn't bother to mess with it because I was leaving for work. So can anyone explain what is going on here? I read the voltage last night based on the terminals I used to jump charge the car. I know the battery is probably toast but why would it say 0v and this morning have the screens come on when I opened the door.

I'm also concerned that I take the car back to the dealership to drop it off and I'll get charged for a new battery