Fog does not affect the sky in Godot 3.x, but it will in Godot 4.0.
As a workaround, make sure the sky is colored in a way similar to the fog. The best way to ensure this is to use a plain color for the sky (instead of a PanoramaSky), and make the sky color be the exact same color as the fog.
Alternatively, you can edit your panorama sky image to add a "fog dome" (a linear gradient that stretches across the panorama) with a color similar to the fog. The same thing can be achieved in a ProceduralSky by changing the colors of its various ground and horizon properties.