2013 Prius (240k) - P148F, P0301, P0302

Hi everyone, looking for some expert opinions on a 2013 Prius Two I just bought used two months ago. It has ~240,000 miles and what appears to be the original traction battery.

My daughter drove it for 1–2 weeks with the Check Engine Light on before telling me. I pulled the codes and I'm trying to identify what might be going on.

Confirmed Codes:

• P0300, P0301, P0302 (Random, Cylinder 1, and Cylinder 2 misfires)
• P148F (Engine Coolant Pump Over Revolution)

Current Clues & Symptoms:

• Starts and Runs just fine: No loud sounds when it starts However, my daughter said that there is a brief, "tick-tick-tick" noise at cold startup that disappears completely after about 1-2 seconds.
• Coolant Levels: The engine coolant reservoir on the far left is critically low (only about 2 inches of fluid left at the bottom). The inverter coolant reservoir on the right is full and normal. Fluid still looks normal and not dirty.
• Pressure Test: I ran the car from a cold start at idle for just a few minutes. When I cracked open the engine coolant reservoir cap, there was a loud hiss of heavily pressurized gas escaping.

I'm guessing that the pressure in the coolant reservoir is combustion gases and I plan to run a combustion gas dye test on it later today. If that's correct, my intuition is that the back pressure from exhaust gases is causing the water pump to cavitate/over-rev, and allowing fluid into adjacent cylinders 1 and 2 overnight causing the misfires.

Do you all agree? Anything else that might cause these symptoms. Is there any chance this is just a cracked EGR cooler? If it's internal engine failure should I try to rebuild/replace the engine or is it a loss at this point?

Thanks in advance for the advice.