What version of SketchUp/LayOut are you using? If 2023 or 2024, make sure you untick the Output Override box in LayOut's Document Setup>Rendering. When that box is ticked, LayOut will render raster viewports as Hybrid or Vector depending on which option is selected. Both Hybrid and Vector rendering result in Vector linework. To show the sketchy line style the viewports must remain Raster rendered.
Example: Same scene with a sketchy line style.
Screenshot - 10_8_2024 , 7_57_26 AM.png