New Battery? Monsoon Flooding? Help appreciated.

Welcome!

It's important to figure out which of these codes are current vs. historical. Based on the immediate symptoms, the warning to pull over, it is likely that the P0A80 is true and current and should be cured with a replacement battery.

The other codes merit a bit more detective work, I think. If the speed sensors got flooded out they'll probably dry themselves and be fine in a few days. And they may already be dry, and these may just be historical codes that can now be cleared/ignored.

I'd be surprised if the rear shocks really needed replacement, they may just be fishing for dollars. That said, $600 is a good price... so be suspicious about what parts they want to use. Toyota dealers are required to use Toyota parts; third parties can use anything they find and lately it is easy to find some really bad counterfeit stuff, unfortunately.

Spark plugs? I think those are due every 125k miles. It could be 100.. Either way 170k is not a multiple of either, so dig deeper on the "why now?" part. $300 is a bit high given the ease of that task. (It's considerably easier in a c than in other versions of the Prius, they may not realize this if it isn't a Toyota dealer)

A 2014 c model asking for a new hybrid battery is right on schedule, to be honest. The battery packs for this model are made to last "about ten years" and they don't really care what the odometer says- use it or lose it. In a drier climate like NM with no winter salt corrosion, it's fair to expect the overall car to last about 20 years, so you're likely to get your money's worth out of a replacement battery.

$3700 is high, but prices have been fluctuating (mostly upward) with tariff news, so there's a lot of new normals to get used to. IMO this is only worth doing if you are using a real Toyota battery. You don't have to pay Toyota to install it, lots of shops can do that and most of them are cheaper than Toyota. Swapping these batteries is not difficult- the c model is probably the easiest in the entire Prius family. But get the part at Toyota.

Check the battery cooling fan under the left rear seat, clean the screen & ductwork. There are youtubes showing the whole thing, you can do it all yourself with a simple screwdriver and the vacuum down at the carwash. While you are in there look for signs of water intrusion from the flood. There is a computer that manages the battery in that general area, and if it got wet from the flooding this could be contributing to the other codes you saw.

Good luck!