Those are two different curvatures you are talking about.

First, you can talk about curvature of the spacetime i.e. treating one temporal and three spatial coordinates on equal footing. Then de Sitter spacetime has constant spacetime curvature, it's basically 4d hyperboloid. Realistic cosmological solutions also all have some spacetime curvature that however is not constant.

On the other hand, in cosmology it's common to consider a slice of constant time getting some 3d space. The time in question is chosen in such a way that everything on this 3d space is to a high degree homogeneous. The resulting 3d space can be of various topology and has some 3d curvature that is completely different from the spacetime curvature. Now the observed cosmology corresponds to zero *3d curvature* but non-zero *spacetime curvature*.

You may ask what would be the 3d curvature for the de Sitter spacetime? The curious thing is how do you define the slice of constant time. The de Sitter spacetime is highly symmetric and you can actually slice it in many ways obtaining homogeneous space. Those possibilities fall into three categories that can be illustrated by this picture (which I made from [this][1])
[![De Sitter spacetime 3d slices][2]][2]
So while de Sitter spacetime has some positive *spacetime curvature* it can be viewed as having arbitrary constant *3d curvature*.

  [1]: https://commons.wikimedia.org/wiki/File:Hyperbo-1s-cut-all.svg
  [2]: https://i.sstatic.net/PvuKF.png