Can someone explain how Kat experienced this part of Tenet from her perspective?

It is a very interesting question, as some of Kat's experience during the car chase is not shown to us. We need to bear in mind that Kat has never been reversed during this entire scene, Nolan dressed her in red as a hint. Below is my understanding from Kat's perspective:

1. Kat is led to the warehouse with Sator and Kat sees an Audi, in which there is a driver that wears oxygen mask.
2. Kat argues with Sator and Sator beats down Kat and spits on her.
3. Kat is dragged onto the inverted Audi along with an inverted Sator (in the forward perspective this inverted Sator is coming from the past towards the turnstile) and an inverted driver. What Kat sees is: everything happens inside of this Audi car is reversed, including how inverted Sator and inverted driver behaves. (this scene is not shown in the movie)
4. Kat is threatened by Sator and the protagonist tosses over the empty orange box to Sator.
5. Inverted Sator and inverted driver jump into a different car and leave Kat in this Audi to die; but Kat is rescued by the protagonist.
6. Kat and the protagonist are both captured by Sator's men and sent back to the warehouse.
7. Kat is given an oxygen mask and led into a blue room and shot by an inverted bullet by inverted Sator. Why a normal Kat needs to wear an oxygen mask? As this blue room eco-system is inverted to accommodate inverted people, therefore inverted Sator does not need an oxygen mask but Kat does.
8. Calvary arrive and Sator escape.
9. The protagonist takes injured Kat into the time machine on their way to the freeport. Now Kat is inverted for the first time in her perspective.

I'm a little late to the party - finished watching Tenet after it was available to stream. I believe while the accepted answer is mostly correct, it doesn't fully address the question; what happened in Kat's perspective. Particularly No.3 above.

I'm gonna use a couple of notations here. P for Protagonist, and the '~' in front of any name to indicate an inverted person. So P is Protagonist, ~P is inverted protagonist, ~Sator is inverted Sator etc.

Let's assume you and I are outside observers who didn't participate in the entire sequence; we're obviously not inverted and witness the whole thing in 'normal' forward moving time. Let's establish a timeline and some hypothetical time stamps for events occurred for our convenience.

9:00 AM --> Sator beats up Kat and leaves her on the floor.

9:15 AM --> Neil and P successfully completes the heist and sees the car ~Sator and Kat are in, on the freeway. ~Sator has an oxygen mask on his face.

9:30 AM --> Kat and P are captured by Sator's goons, and taken into the turnstile building; Kat from the Blue side and P from the Red side. ~Sator puts on an oxygen mask to Kat's face, in awkward backward movements. ~Sator himself already has an oxygen mask on his face.

9:45 AM --> P is questioned by ~Sator from the Blue side of the turnstile building, and Kat is shot.

10:00 AM --> Ives' team bursts in, Sator (who's on the Red side) runs through the turnstile and inverts himself to be ~Sator.

So above is a list of made-up time stamps from our outside perspective of what happened. Now you asked what it looked like from Kat's perspective. This is tricky, but we can break it down. As correctly stated, Kat was never inverted at any point during the above timeline. So this means everything she experiences is the same as you experience in normal forward timeline, even when she's held hostage by ~Sator and is inside the Audi.

So based on above timeline, we know Kat was beaten up and was on the floor at 9 AM. Then while she was being held hostage by ~Sator, although ~Sator is moving backwards in time, Kat is not. So, what looks like the beginning of the car chase for ~Sator is in fact the end of the chase for Kat.

From her perspective this is what Kat sees:

1. She's lying on the floor after being beaten at 9 AM.
2. She's being held hostage in the car at 9:15 (here she sees ~Sator and ~Driver doing everything backward, she will see the car she's in running backwards, while she sees P in the other car doing normal movements).
3. Kat will see herself captured by goons at 9:30 and then handed to a ~Sator walking backward who then proceed to take her through the airlock into the Blue side.
4. Shortly after she will see ~Sator putting an oxygen mask to her face and taken into the blue side, still ~Sator walking backwards. She will see P seated in the Red side.
5. At 9:45, she will see ~Sator question P, then ~Sator will 'un-shot' a bullet through her body into his gun.
6. Then she'll be left bleeding on the seat, and she'll see ~Sator remove his own oxygen mask, and she'll see ~Sator disappear into the turnstile at 10:00 AM.
7. She'll see a bunch of TENET team walking into the Blue side (but they are not inverted and walking in normal fashion), put her on a stretcher, and take her out of the Blue side airlock (NOT into the turnstile).
8. She'll see herself being wheeled on the stretcher to the Red side, then P and Ives argue, they all decide to go in through the turnstile this time to invert themselves including Kat.
9. They'll all emerge from the Blue side, say at 10:15, inverted.

Now, the real mind-bending question is how did Kat, who was on the floor in the turnstile building from 9:00 to 9:15, get into the Audi with ~Sator at 9:15, presumably miles away from where the freeport is. I think the explanation here, although not shown, is that she simply disappears from turnstile building at roughly 9:15, and appears out of thin air in the Audi alongside ~Sator. I know this is quite hard to wrap your head around because it's a person involved, but we see similar things happen to object (or even people) throughout the movie.

For instance, in the car chase itself, shortly before Neil and P sees the Audi ~Sator is in, we are shown a shot of the side mirror of the BMW that Neil is driving and we can see that it's broken. Then when the car BMW collides with the Audi, we can see the broken mirror gets repaired. So... at what point did the mirror broke before it got 'unbroken' by the collision? Well, obviously it wasn't broke from the day car was manufactures, and in fact the mirror just simply broke suddenly shortly before that. Because it has to be broke in order to get unbroken. Same way, we see that when ~P is going back to Oslo freeport with ~Neil, we see that a wound appears out of thin air on ~P's arm and he starts bleeding. So basically his intact skin suddenly got wounded without any outside contact, because it needed to be wounded in order to be 'healed' by P 'un-stabbing' himself.

Same way, once we buy into the premise that inverting entropy of an object (or person) makes them go back in time, we must also buy into the premise that objects or people can appear and disappear in order for inversion to work. This is why Kat can disappear and appear, because the events happened in inverted timeline of Sator dictated that she needed to be in the freeway at 9:15 in the car with him.

If you really do not like that explanation, then we can go for a safer second explanation: at 9:00 AM one of Sator's non inverted goons put Kat in a car and drive her onto the freeway, and at 9:15 AM just before P and Neil see ~Sator and Kat in the car for the first time, the goon transfers Kat to ~Sator's Audi.

Basically, not just the characters, but we as viewers must also stop thinking in linear terms to fully understand (and appreciate) Tenet.

The audi was right outside the warehouse when Kat was initially brought there by volkov and Sator. You can see the Audi on the other side with the inverted driver inside.. So from Kat's perspective she was just taken straight into the Audi from the floor after she was beaten up. From Sator's inverted perspective, he and his driver were simply dropping her off after the whole car chase (from an inverted perspective)