Prius Gen 3 - Braking Issue

This is usually a bad ‘brake actuator’, and the buzzer means it is unsafe to drive.
What year and how many miles?

 

There is an electric pump that operates when needed to keep a supply of highly-pressurized brake fluid to assist your effort on the pedal. The sound of that pump is probably what you are thinking of as the "sound of the brake actuator".

The actuator does also make some sounds, but they are mostly rather soft clicky noises and usually you don't hear them.

If the pump doesn't run, that would explain you not hearing the pump noise, and it is not keeping the fluid pressure up, and the buzzer you are hearing is because the pressure is too low, and the brake being hard to press is because the pressure is too low to assist you.

So everything in the picture fits together; this isn't any kind of obscure or baffling problem. Other people can have different problems where the pump does run but the pressure doesn't hold because of leakage somewhere, but you seem to have a simpler story.

The main thing you want to do is find out why that pump won't run. It could be somewhere in the electrical supply to the pump (wiring, fuses, relays) or the pump itself. The pump itself is (a) kinda pricey and (b) a knuckle-buster to replace, so I would not jump to replacing it before being sure it's at fault.

The trouble codes in the brake ECU will help you: I wrote a post a few years ago that was exactly about how extensively the computer monitors that pump to be able to give you good troubleshooting assistance. (That post was about Gen 1 so the Gen 3 details will differ some, but the ideas are the same).

If you're not getting any of the codes from the brake ECU, you should see if you can get access to a laptop with Techstream so you're not forging ahead without that information. If that isn't convenient, you can get the brake blink codes using nothing but a short jumper wire. They will be two-digit, abridged versions of the codes you could get with Techstream; it will be strictly less information than Techstream would give you, but still beats taking guesses in the dark, and the best part is it works any time, even when you don't have a Techstream rig handy.

Pace bisco, the cases where the cause might be the 'brake actuator' are the ones where the pump runs but the pressure doesn't hold because of a leaky valve (which, odds are, will be in the actuator, just because that's where most of the valves are), but in your case if the pump just ain't running, the lack of pressure is already fully explained without dragging the actuator into it, and the actuator is probably fine.

 

Call a Toyota dealership as soon as possible and get them to replace your master cylinder and related components under extended warranty ZJB - I am 99.9999% sure you will qualify. Even if you don't have the warranty letter, they can look up your VIN which will show all the warranties and recalls that apply to your car. From the sounds of it, your car is not safe to drive and should be towed to the shop.

From Toyota itself: "Toyota has received reports about certain internal malfunctions of the brake booster assemblies..." This is a serious issue that is currently being reviewed by the NHTSA.
Toyota Brake Booster Recall Needed, Says Defect Petition | CarComplaints.com

 

Certainly no harm in checking with the dealer. If you do, please follow up here with the outcome and/or what they determine to be the problem.

From your comment in post 1 that the pump apparently isn't running at all, I would not be too surprised if the dealer chooses to focus on that rather than the ZJB issue. But if they do decide you qualify, and it fixes the problem, it's hard to argue with free.