I can't find much about Pearl Star Leghorns, but my first question would be: if they actually have Sussex and Barred Rock parentage, why would anyone call them "Leghorns" at all?
I do see a hatchery that says the same thing you found
https://townlinehatchery.com/product/pearl-star-leghorn/
"One of our most popular breeds for large cream-white eggs and variegated feathering. Townline’s Pearl Star Leghorns are imported from the Czech Republic and are a cross between Partridge Rocks and Sussex."
If they are laying "cream-white eggs" and are called "Leghorns," then they cannot really come from just those breeds, so there is something weird going on here.
As regards the chick in your photo, I agree it cannot come from the parents in the picture on that hatchery page.
Your chick probably has white barring (light spot on top of the head when hatched), and I think it is probably blue (based on the color of the down.)
I think you are just going to have to see how it looks as it grows.
Here are two older threads on BYC that talk about "Pearl Star Leghorns":
https://www.backyardchickens.com/threads/pearl-star-leghorns.1349837/
https://www.backyardchickens.com/threads/pearl-star.1566342/
The longer one of those threads has some photos of birds (that do not look like your chick), and also has a link to this page:
https://www.dominant-cz.cz/en/programs/white-and-cream/detail/137/dominant-brown-d392
The thread says that "Pearl Star Leghorns" are from the breeding program on that page (which does not exactly match what the hatchery said!)