Title basically. I tried to underexpose the shadows severely to make it look more the silhouette, but that just made it look even worse. I suppose the only way to get better pics is to find a better location. But I would appreciate if someone can give me advice on any other tricks I could use to make the sky look better and take focus away from the urban hell

Glad you enjoy ddoi!
If you can’t get out on that balcony, backing up and introducing your window/doorway as an artificial frame could also add depth/interest.