A Spotify support page explaining how to use the web player includes a list of supported web browsers, which has been updated to include Apple’s browser alongside Chrome, Firefox, Edge, and Opera.
Previously, users who visited the Spotify web player on Safari received the message, “This browser doesn’t support Spotify Web Player. Switch browsers or download Spotify for your desktop.”
Spotify confirmed the incompatibility between its web player and Safari in September 2017, but never fully explained the problem. One theory was that it had something to do with Google’s Widevine media optimizer plugin, which Spotify used for music streaming on the web but Apple opposed on security grounds. Whatever it was, the issue now appears to have been resolved.