Birds adapt their song to ambient noise conditions. This paper [1] studies the Pearl River Delta (where Shenzhen is) as a natural experiment. It shows spectral changes in the target species correlating to background noise levels. I haven't looked hard enough to make sure there isn't a study that does find complexity changes but it's certainly clear that noise can affect bird song behavior generally.
[1] https://www.sciencedirect.com/science/article/pii/S235198942...