There are times when applications add a new groundbreaking feature that surprises us, flabbergasts us, elates us, and makes us go "wooooow, that's really cool!" This is not such a time. Instead, we're here to talk about Spotify adding the basic of most basic features of any music or audio playing app: a sleep timer. It's 2019 and this has just happened. Miracles, my friends. Don't stop believing.
To set up a sleep timer, tap on the overflow (three dots) icon on the top right of the Now Playing screen in Spotify, then look for Sleep timer. Choose between 5, 10, 15, 30, 45, and 60 minutes, or until the end of the currently playing track. Your timer will be set and the countdown will show up in the same overflow menu. You'll see Sleep timer - 27 min left for example, like in the screenshot below. When the time has elapsed, the music (gasp) stops. It's groundbreaking.
I'm seeing this on the latest Spotify v18.104.22.1689 but it's possible the feature began rolling out earlier to some users, or that it's still not live for everyone.