Why are static light baked shadows are so pixelated compared to stationary?

By default, stationary lights store their static shadows in a separate texture as a 2D distance field which allows them to generate sharper shadows at lower lightmap resolutions.

One of the side effects of this is that you can’t get area shadows from them, which is why you can disable the 2D distance field generation by enabling “Area Shadows for Stationary Lights” on the light you want to have area shadows, or there is a project-wide setting in project settings for distance field stationary shadows. If you set (or unset, in the case of the project setting) either of these then the resulting shadow will look like a static light.

Static light shadows are baked directly into the primary lightmap and so they can’t be stored as distance fields.

It will primarily affect build times for you and GPU memory and size on disk for the end user, may also impact streaming performance. If you use SVT lightmaps it probably won’t matter to the end user other than size on disk.