You have a continuity problem based on the triangle interpolation. The following statements are not necessarily true for all interpolation models, but should be for the basic linear interpolations done by the GPU:
If you have a triangle with 3 colours at the nodes, than each node will contribute to the final colour as long as you are not on the boundary. If you are on the boundary, only the 2 nodes that form that boundary will contribute.
If you have a rectangle with 4 colours at the nodes, than each node will contribute to the final colour as long as you are not on the boundary. If you are on the boundary, only the 2 nodes that form that boundary will contribute.
Comparing these two statements gives the following conclusion:
If you split up a rectangle into two triangles, the interpolated values on the outer boundaries stay the same. However, the surface in each triangle is only interpolated with 3 values instead of 4. Additionally you create another boundary (the diagonal), which means that you interpolate only two points there, while the rectangle uses 4. So in your picture the diagonal values are only composed of green and blue instead of red, green, black and blue. The same problem holds for the normal interpolation.
As said before, this is a continuity problem. The interpolation you (or the GPU) use has C0 continuity. This means that if you would do a mathematical plot of the interpolated values the resulting curve has no gaps/jumps in it, but it might contain visible kinks (located were the boundaries are) because its first derivative can have gaps/jumps. Its like a car that drives with 10km/h and its speed suddenly jumps to 30km/h with no acceleration phase in between as soon as it passes the boundary. Even though its position (C0) does not jump, its velocity (C1) does which would result in a kink in a time-position plot.
So how to solve that?
The best solution would be to use an interpolation that is C1 contiguous. This can normally be achieved with splines/NURBS. I am not sure if this is possible here, since it requires higher order interpolations of triangles, which is not possible to my knowledge. Maybe one of the more experienced users can give a statement on that (Curious if it is possible in Vulkan…).
The second possibility woul be to use higher order triangle interpolation without splines/NURBS, but the same question as before remains.
The third and last option I know is to simply subdivide your mesh (as you suggested), until the the kinks are barely noticeable.
The combination of the second and third solution is known as h-p-refinement in case you want to know more about it.
Hope I could help you a little to understand what’s going on.