2013 Prius Touchscreen issues

Hey everyone! Long time lurker, first time poster. I have a 2013 Prius Two that's hit about 133k miles. For a few months now, I've had an issue with the touchscreen/buttons and it's finally gotten to the point I can't touch anything on the screen. I have the stock head unit with no custom modifications.
It started with the screen randomly 'pressing' buttons on its own as I'd be driving. Usually, when I'd be in a turn, it would do things like set the station I was listening to on the radio to whatever slot the preset was on or change the mode to AM/Bluetooth. If I was in the phone dialer, it might type 5555555 or 6666666. During this time, I found I could not use the touchscreen at all. If I were to push the volume up/down button on my steering wheel, it would stop this and I had control of the touch screen again. It was pretty rare it happened, maybe once a month or so,
Then it started to become more frequent. I found I had to push the volume up/down a lot to get the screen to unlock from whatever was holding. Sometimes, even when I unlocked it, I couldn't press certain areas of the touchscreen. And other times, after unlocking it, it would almost immediately lock up again. It was annoying, but I just lived with it.
Finally, it all came to a head last week when I went on vacation and left my Prius at a friend's house. They moved my car while I was gone and accidentally left an overhead light on which drained my 12v battery. The battery was old and draining it finally killed it as the battery would not keep a charge after a few hours of the car being off, so I went ahead and replaced it with a new OEM one (lasted 10 years!). But, now the touch screen does not work at all. All the physical buttons still work, including the steering wheel ones, but the touch screen will not register anything at all. Doesn't matter if I use the volume up/down. The good news is that it doesn't randomly 'press' buttons as it did, but I can't do any on-screen functions.

So the question is... what caused this and what died? Was it the touch-screen? A short in the steering wheel buttons? My Prius is pretty up there in miles, but I think she has a lot of life left to give. As such, I'd like to get this fixed. If it's as 'simple' as replacing the touchscreen, then I would dive into that or even put in a new improved third-party head unit. But if this issue goes beyond that into the steering wheel, then I feel I'd have to take it to Toyota to get fixed.