Firstly, the apartment is as pictured on Airbnb. It has great functionality + aesthetics + central location. Thanks Alex.
However personally, myself and my girlfriend had our sleep disturbed continuously at the apartment, and wouldn't want others to go through the same experience. Clearly some people can sleep through anything, so the following isn't for them. The rest of this post is for those who like going to sleep with quiet.
The noise mainly comes from the bars outside the apartment + people who use the street to get from A to B. Friday and Saturday night were particularly bad, with loud conversations + shouting taking place on the street. Friday we were kept awake from midnight - 5am.
Additionally each night (except Sunday) at around 1am, garbage is collected outside the apartment. Meaning you can hear loud crashes and shouting whilst this takes place. Some nights this takes place multiple times. And can be the straw that broke the camels back, if you've just managed to get to sleep from the street noise.
I wouldn't consider myself or my girlfriend as light sleepers, but even with earplugs, we got disturbed continuously.
Then because of the apartments poor sound insulation, you get the noise of dogs barking and loud talking coming from people in the same apartment building.
My guess is that if you're planning to go out in Madrid, and get back late, then the noise is less of an issue. But if you plan to have busy days exploring Madrid, and need your sleep, be warned.
In retrospect, I'm grateful for the experience. I now appreciate how important having peace whilst sleeping is for me. Will try to avoid making the same mistake twice.