Advice for parent's 07 Prius: P3000, P0420, P0A80, C1311

Hey everyone, my parent's 2007 Prius with 245,000 miles is finally showing signs of a failing traction battery. Up until now, they've been going strong on the original battery. Along with the traction battery codes, Techstream is also giving me code P0420 "Catalytic System Efficiency Below Threshold (Bank 1) which is concerning.

My father just put new snow tires and brakes on the car, so he's weighing his options a bit. I have a local reputable hybrid battery specialist who could either a) install in a junkyard battery or 2) install a 3rd party reconditioned battery. I'm aware of the implications of these reconditioned batteries, as I have already done so on one of my previous cars.

Personally, I don't have the patience or time to mess with swapping cells; so my main concern / question right now is the P0420 code - is this possibly related to the failing traction battery? Or are we looking at needing to replace the CAT at the same time as the battery? If indeed a replacement may be needed, at that point it likely won't be worth putting the money into this car.

Advice would be appreciated.