The SkyLIght HDRI is something different that Sphere that you are using for background.
Skylight is the real emitter but that Shpere is only a background texture put on the huge sphere object to mimic the world.
Remember that you have to rotate Skylight HDRI via its special rotation parameter called Source Cubemap Angle ( and rotation direction is opposite to the rotation of all objects in scene - surprise ?!!! ).
If you want to have Sun “visible” via your room hole you need to rotate SkyLight HDRI by using that parameter.
So if you for example see the Sun on background Sphere map via your hole then try to rewrite Z rotation value form that Sphere to the Source Cubemap Angle with MINUS.
Then you should see the shadow after bake.
Unreal is not so easy and full of nasty surprises created in dark developers minds