check engine light + soft whirring noise

Open the hood and listen for this noise. The brake actuator sound will be coming under the windshield area. The coolant pump and all are close to the front of the car.

 

If you want to determine the life/state of the hybrid battery, use the Dr. Prius software and a proper OBD II doogle interface for a reading the data by a phone. Useful for controlling the hybrid fan, as well. Then test the battery following the instructions. It will tell you what you need to know about that battery.
As for the ABS system, if no codes, why replace it? Wait for codes to show. I assume the brakes are working fine - that is an easy test if in doubt.
The inverter coolant pump is easy to tell if working. Remove the coolant cap (for the inverter coolant, NOT the radiator!) You should see motion of the fluid. If not, the pump isn't working.
Definitely, if the valve was still bad, the code should quickly return.

 

The car has a ODB II port under the dash on the drivers side. It is easy to see if you look where the photo shows in your car, you'll see it.

 

You buy the dongle that plugs in that works for Dr. Prius (their web site explains details) and it shows the hybrid batter charge and many other details on your phone. If you pay for their software upgrade (about $15) to add to their free software, you can test the hybrid battery's condition. They have examples online to watch on youtube.

By testing the hybrid battery, you'll then know its performance/life-time and if that is an issue that will cause problems sooner rather than later.

 

No, the brake actuator/booster/master cylinder pump does not normally run constantly.

When it was new and for years later, you might hear it when you approached the car or touched the door handle for the first time each day.

When it runs every 3-5 seconds or keeps running you might be closer to a brake booster replacement. It is not cheap, maybe $2,500 installed at a dealer or a quality independent shop, primarily because there are no rebuilt or aftermarket alternatives.

For most of the population who don't know an obd2 port from a brake booster, the best thing to do is to spend a little at the dealer or quality independent hybrid shop for a diagnosis. Without warning lights, this is for your own peace of mind.

Then come back for recommendations for budget options before paying a dealer to repair. This step is important because a dealer may offer unnecessary "preventative" services like fuel system cleaning, alignments or early fluid changes.

 

I've always heard the brake pump as a buzzing noise

 

All you have to do is open the hood and see if the noise is coming from the driver's side under the windshield-wiper.

 

Here is a gen2 engine with hidden brake booster area highlighted.

 

Looks so clean.. almost brand new..

 

An auto parts store will have a thing called a mechanics' stethoscope, maybe around five dollars, with ends you put in your ears and a long rod you can touch to various things under the hood, and you'll quickly pinpoint the source of the sound.

If there's no mechanics' stethoscope around, a long stick or screwdriver can work nearly as well, with one end touched to something you want to hear better, and the other end pressed to the bone under your ear.