Thanks for coming to the Spotify Idea Exchange and voting to make this happen.
We're happy to announce that the option to manage Autoplay has been released for the desktop and now for the mobile app too.
Once you have the latest version installed, you will find it as "Autoplay on other devices" in the Settings menu and it will apply globally for connected devices and the web player.
Note that you will need to log in and toggle the setting on or off on either the PC/Mac or Smartphone apps, but once done you can continue using Spotify on whichever platform you prefer and the setting you chose will be reflected accurately.
Once again, thanks for helping us make Spotify better, by participating here on the Community.