As the title says, when you set a skylight to static it no longer casts reflections on the scene. I get that static lights are supposed to only really exist during light baking, but skylights serve the important role of providing fallback reflection data for surfaces outside the influence of reflection captures and SSR. Without it, you get zero specular highlights in some areas (or lots of them, depending on your scene).
It’s possible to use a large reflection capture covering the entire level to make up for it, but that is a bumpy solution: unlike skylights, reflection captures don’t have a setting to render only distant geometry and to set the lower hemisphere to black. If you’re using an HDRI cubemap for your sky and skylight, it’s just a matter of setting the capture to use it as well, but if you’re using a captured cubemap you’ll end up with some of your level showing on the reflection and need to resort to some trickery to get it looking right.