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Thank you!

This is indeed Delaunay triangulation, barycentric coordinates, linear RGB and projections on the edges for the points outside of the mesh. You got everything right!

Having a nice blending along the edges doesn't seem straightforward. I have a few options in mind but nothing obviously right (working with a voronoi diagram instead of a delaunay one, bezier interpolation)

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Maybe a single pass of root-of-3 subdivision would already help? It would insert another "control point" at the middle of the existing triangles. Then you could linearly interpolate along the new refined triangles. That wouldn't really remove the saddle points (if my intuition is correct it would just divide them into smaller ones along the new triangles), but maybe they'll end up more smoothed out and therefore less jarring.

[0] https://www.graphics.rwth-aachen.de/media/papers/sqrt31.pdf

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