Inverter cooling pump and HV battery fail simultaneously

I have an 07 2nd gen Prius 162k miles and original HV battery and new 12v battery. I have an issue that I haven’t found described elsewhere specifically. I had a couple isolated incidence over the last couple months of multi system triangle, VSC, yellow exclamation and check engine, lighting up while accelerating from 60-70mph but no perceived change in performance. The warning lights would go out by the time I could get an appointment at the dealer. Then it happened at 25mph and have stayed on.

Found out the two error codes were inverter cooling pump fail (confirmed by no turbulence in fluid reserve) and second code was replace HV battery. According to energy monitor, car appears to be charging and using EV power, but the engine remains on constantly (driving and in park) even when battery fully charged on energy monitor screen. The battery fan comes on and stays on once driving. Only performance issue is car doesn’t feel like getting supplemental power from the EV system.

Last week before errors I was getting 41mpg of mixed driving highway/local.

How likely is it that both pump and battery failed simultaneously?
Could the pump failure be causing the HV battery failure? It doesn’t seem logical to me that HV battery fail could cause pump fail, also, car doesn’t display symptoms of other users who have HV battery failure.

Any input is appreciated.