It means the static mesh asset does not even have a collider. Double click the asset and add a collider. Or use a blocking volume as a collider while the mesh serves as a visual indicator only.
When it comes to a Pawn with multiple meshes, you’d need to rely on physics to detect collision and use sliding collision. It will work OK with a floating movement component. As in, you expect this, right?
Default collision settings, only the root component simulates physics.