2007 cat stolen, hybrid batt, and more! Keep the car?

Hello all! I've got a sad Prius story to share and need some advice...

My fiancee and I are both students at UNC and were home for ~2 months over winter break. When she came back to her 2007 Prius that was sitting in Chapel Hill, we found that the cat was stolen - got that fixed (aftermarket) but now we're still having issues with the car.

We've got the classic Christmas tree of warning lights for the hybrid battery (code P0A80) and were quoted $2750 by the dealership for a brand new replacement. This wasn't a huge surprise after letting the car sit for ~2 months and after 160K miles, but still disappointing. However, we're also having more problems with the car that don't necessarily seem related to the battery. The car is still drivable, but will randomly shift from driving normally with weak acceleration to having a very high idle and almost no acceleration at full throttle. After restarting the car at a traffic light or parking lot, it's back to "normal." She's also burning a good bit of oil.

At this point we're trying to decide next steps... it feels like a bit of a gamble to invest in a new battery when there might be additional issues with the engine. Is the high idle/acceleration issue related to the battery or something else? Do you have any advice on replacing the battery vs. getting a new car?

Thanks so much for your opinions, any and all help is appreciated!