Actually, the notion that it's Sakura's sacrifice is correct! This is actually explained at the beginning of xxxHolic volume 2, chapter 8, which covers the same event of the four travelers showing up at Yuko's shop, but from the xxxHolic side of things. I'll quote Yuko, and for convenience I'm just going to ignore Watanuki's dialogue in between her lines (it isn't any less clear without it anyway).
"There are actually four people Mokona Modoki is taking on a journey through the worlds. Sakura-chan is one of them. In other words, Sakura-chan has to pay the price for the wish, too. But she left her kingdom with nothing but the clothes on her back. She has nothing she can pay with. And even though her memories are scattered across the worlds... the one thing that is most important to her is her memory of Syaoran-kun. Yes. That is the price she pays. She is the person for whom the help of Mokona Modoki is most urgent. And so, the cost to her is the greatest. And in truth, I should have demanded all of Syaoran-kun's memories of Sakura-chan as well. But... this is enough. To have the person most important to you forget you completely... It turned out that Syaoran-kun paid the price with his most precious relationship. I let them off easy. I'm just a big softie."
And there you have it! It really was Sakura's sacrifice, and Syaoran was actually able to get off easy because Sakura's sacrifice is so big. And to be clear here, I don't remember how the anime words it, but the manga of Tsubasa and xxxHolic uses the word "relationship" to describe what he's sacrificing. He is sacrificing his relationship with Sakura. So, going off this quote, it can be thought of as an overlapping sacrifice between Sakura and Syaoran.
So, Funimation, if you ever play that commercial again you better change it to "Her soul. Also her sacrifice."
