If you are on PC you can install the EHT add-on. The rugs (really anything) in EHT FX do not reflect or interact with light in-game the way standard furnishings do.

So you would have to put an EHT rug (or map or grass or anything) on your floor over the place where the light appears. There are lots of options. Whatever looks ok.

That is what I do.

Someone had a game technology explanation for it a few years ago but I have since forgotten what it was. It was about fireplace light bleed specifically. If it were less of a chore, I would post screen shots here to show you what it looks like.

EHT is a very nice add-on in many ways. You can do actions and scenes with it too, but if you try to do tricky stuff with those be prepared for some head scratching.

If you are not on PC then I have no advice.

The reason that the lighting effect still goes through the wall that you put there is probably because you placed it close to the window. Aka, the window is inside the furnishing that you used to cover it, so the lighting effect only has to go through the inside of that item. Most items don't have textures etc on the inside, so the game thinks that the light can pass right through it.

Solution? Use a carpet in front of the window. The carpet should be thin enough to end up in front of the window, but remain hidden inside the object that you actually use to hide the wall. Pretty much any carpet will do, but I'm partial to the cheap breton rugs myself.

There are however a couple of windows in the game where this doesn't work for some reason, and light will come through no matter what. Hope that helps!