Spotify’s Web Player is not available on Safari due to a “recent update” of the web browser, and people have to change another web browser if you need to use this service.
Recently, many Spotify users posted comments on the forum that they can’t use the Web Player on Apple’s Safari browser, and receive a message “This browser doesn’t support Spotify Web Player. Switch browsers or download Spotify for your desktop.” Soon after, Spotify customer support confirm the removal of the Web Player on Safari, and explained:
“After taking a look backstage, we can confirm that after recent updates Safari is no longer a supported browser for Web Player. … We can’t say if or when any specific features will be back. But as soon as we’ve got anything to announce, we’ll let everyone know via the Spotify Community. Sorry again for any inconvenience caused, and please let us know if there is anything else we can do for you. “
So you will need to change the web browser to use Spotify in recently, and Spotify also encourage users to download the compatible Spotify app for Mac.