I am using the Spotify Web App and the private session option does not appear in the top-right dropdown menu nor does it appear in settings. (In fact, nothing is in settings aside from the language selection option)
Hey @Noctswife
The Spotify Web Player does not currently have the Private Listening feature.
To use the Private Listening feature and all of the other more advanced features you will need to download and use the Spotify desktop app.
You can download the full Spotify desktop app here:
https://www.spotify.com/download/
The desktop app also has a lot more settings listed on the settings page.
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