This is a remake, not a remaster. This part will be rebuilt from scratch in the AnvilNext 2.0 engine, also known as the engine that runs the last few parts of Assassin’s Creed.
When (a lot of) negativity came out about the trailer and the screenshots, the developer explained why they made it look like this: link
From that article it appears that it has to do with the fact that the AnvilNext engine is intended for open world games, and they had to rewrite it in such a way that you can also make a more linear game like Prince of Persia with it. They also say that it has nothing to do with the budget:
“No it was not a problem of timeline or budget,” says Syed Abbas, Deputy Managing Director. “For us at Ubisoft quality is of the utmost importance and this is something that we have kept in mind from the start. The project has been in development for the last two and a half years. We have had at peak 170 members working on this project and not to mention other investments in infrastructure and set up to make a modern game. No there have not been any cutback in budget or timeline for the game.”
IMO: I think they delayed the game to release it soon on the XBONE and PS4, but also with all registers open on Xbox Series X, PS5 and PC