Car pulls to the right (three alignments done)

welcome!
have you tried rotating the tires?

 

Does it matter what road you're on? Most roads have a high crown in the center for drainage, so with a right-hand traffic pattern there can be a noticeable rightward bias induced by the road itself.

Does it feel different in a flat parking lot?

 

In my experience, dealers are not expert in alignment issues. They put it on the rack and the alignment came back OK. They haven't checked everything, since the problem still exists. A good independent shop with suspension expertise is your best bet.

You can get what's called a "radial pull", where a tire causes the pull. This can normally be eliminated with a tire rotation, particularly moving the problem tire to the rear. Rotating the tires would be my first step - this would rule out a problem tire.

It could be a problem with the steering rack - failing to self-center after a right turn could be wear on that area of the rack.

 

Unless Toyota did something exceptionally unusual for your model, the return-to-center property of the steering system is completely passive. No dependency on the power assist system or the electronics associated with it.

Dragging brake?

 

This is why you take it to a shop that does more than alignments - i.e. an actual mechanic. I would be done with that dealer, since they have proven they are at a dead end. They will fire up the parts cannon at your expense, but without basic troubleshooting and systematic elimination of potential problems, you will be wasting money.

Or a mechanical problem in a tie rod end, ball joint, etc. I would lift this car on a rack or the front on stands and test it unloaded for steering centering, binding or loose parts, etc. Check brakes at same time. If you can't duplicate the problem, then it is a loaded problem, so they start looking at things that carry load.

 

In my experience, dealers are not expert at ANYTHING these days except taking your money.
If the computer doesn't give them a code or codes that point only to ONE defective part.......they likely will throw up their hands and give up.

This problem could be:
Dragging brakes.
Loose or worn parts in the suspension.
Loose or work parts in the steering mechanism.
Worn wheel bearing.
And probably several others too.

AND.....the problem might actually be in one of the REAR wheels too.

In order to find the problem, they might actually have to LOOK at some likely culprits to see what is going on.

 

So I too have a Gen 3 Prius and have a very similar situation (which brought me here). I've been irritated for a long time with intermittent pull to the right. Though, I haven't narrowed down whether or not it's fine after a left turn as you have, just that it isn't constant pull to the right all the time.

I had an alignment done with new tires and they said the alignment wasn't the problem and that I wouldn't even notice the little adjustment they made to it. This slight pull has persisted throughout the life of those new tires, and I just got a new set that are doing the same. It's beyond clear to me that there's an issue elsewhere.

I replaced both rear wheel bearings because it feels like the car has some extra drag/resistance to it.

The suggestion from Sam Spade with the brakes dragging is exactly where my head is at too, though I don't know what the hell to do about diagnosing/fixing it yet.

I also have one more kink in my situation that I very much so doubt applies to you, but you could have a natural failure in the same component... I'm doubting the below is relevant, but in case brakes aren't the cause:
When my uhhh, 'friend' did my brakes, he used one of those bleeder's with the bottle that has a magnet on it, and he stuck it on the rim. 'He' didn't realize that the magnet had detached from the bleeder bottle before re-attaching the rims/securing the lugnuts, and I only discovered it after another driver told me my right-rear real was loose while cruising down the road at 60mph. When I took the wheel off, a shattered magnet was discovered. I'm wondering if this could have really dicked up a more serious component in the suspension, which is leading to drag.