Propper Scene Sun with shadows

Hey there,
I grow a bit desperate (again) trying to set up a Sunlight in my scene that casts shadows… simple shadows… looking at what is possible nowadays I thought this should be a no brainer.

So I set up a directional light and it, unfortunatly did not, what I wanted.
I set a target to the light, an empty in my scene, but there only very fuzzy shadows on very small part of the map…

Is there an addon, or so, any way to just add a Sun and it casts shadows everywhere… something like this?
Here is the Code I used for the light:

const directionalLight = new THREE.DirectionalLight( 0xffffff, 0.5 );
directionalLight.castShadow = true
directionalLight.shadow.mapSize.width = 512; // default
directionalLight.shadow.mapSize.height = 512; // default
directionalLight.shadow.camera.near = 0.5; // default
directionalLight.shadow.camera.far = 500; // default
scene.add( directionalLight );


This is what it looks in my scene:

Set up a DirectionalLightHelper to see the frustum that the directional light is covering. You want that frustum to match your scene as tightly as possible to maximize the shadow quality… both in size and depth.

You can adjust the dimensions of that frustum with:

directionalLight.shadow.camera.left =
directionalLight.shadow.camera.right =
directionalLight.shadow.camera.top =
directionalLight.shadow.camera.bottom =
directionalLight.shadow.camera.near =
directionalLight.shadow.camera.far =

followed by directionalLight.shadow.camera.updateProjectionMatrix();