Why does the Ash Twin Project require rotation for artificial gravity?

The "conventional" way of generating some kind of "artificial gravity" (any kind of force that is perceived as pushing you down on the ground of some space station or whatever) in a science-fiction setting often is huge rotating rings, where the centrifugal force you would experience in a rotating reference frame pushes you away from the point the ring is rotating around, and thus pushing you on the ground of the ring-like structure.

For example in '2001: A Space Odyssey', there also is a station that consists of two huge rings.

I never played Outer Wilds myself, but this wiki article says that "The surface of the platform is made entirely of gravity pads, ensuring that the player does not fall off.". So that would mean, that it's actually the same technology the Nomai used elsewhere.

Which in turn means, I can't actually give you a game-specific answer, only the general, "out-of-universe" answer how a rotating ring would "create" something you would perceive as gravity when standing in the ring with your head pointing inwards and you feet pointing outwards.

The idea of a spinning ring acting as some kind of centrifuge is also illustrated really well in this video by the YouTube channel "Real Engineering".

Maybe the Ash Twin Project was started by the Nomai of the Ember Twin (since they were closer than the ones in Brittle Hollow), and I don't remember any platform of gravity in Ember Twin, they only knew the rotation method you mentioned and they applied it inside the Project.

I think the Nomai in Ember Twin didn't know about the gravity platform technology, the rotational method was the way to go, and since it was started with the rotational technology it wasn't interesting to change the mechanism at all since it was working that way. I'm sure they debated the idea.

For an out-of-universe answer, I think the interior of Ash Twin was designed to have a interesting, mysterious visual when viewed via its Projection Pool using a Projection Stone. I think the developers wanted players to wonder whether they were seeing a real place or something metaphysical. Using rotation helps with this goal:

• The only lights you can see are the three glowing masks, the starry background, and energy moving through the solar panels to the core. If a gravity floor were used, the player would also see the glowing purple lines that are part of all gravity floors, lessening the mystery. Similarly, gravity crystals glow in the dark and would also lessen the mystery.
• The speckled stone shell that is rotating relative to your viewpoint looks like a moving star field. If the Ash Twin Project interior didn’t move, it would be easier to tell that those “stars” were a static background. Without rotation, you could move your character around within the Projection Pool platform and notice that the “stars” move a significant distance when your viewpoint moves.

Additionally, the developers probably wanted the Ash Twin Project to be memorable, as it’s the central mystery of the game and entering it is an important moment in the story. One way to make it memorable is with a unique mechanic. Rotation provides the room with a unique navigation puzzle and physics showcase.