Hi @Lee01,
Thanks for posting in the Spotify Community, and welcome!
If you’re using the desktop app, the settings to prevent automatically publishing playlists to your Spotify profile, to not share your listening activity on Spotify with the users following your profile, and to hide your recently played artists on your profile should show up in Settings under Social:

You can toggle these settings to “off” (gray instead of green) so that your friends won’t be able to see what you’re listening to or see new playlists that you create on your profile.
Also, if you already have public playlists on your Spotify profile, you can remove them from your profile by following the steps in this support article.
It’s also worth mentioning that you can temporarily prevent anyone who follows you on Spotify to see what you’re listening to with the Friend Activity feature by starting a Private Session. This FAQ article provides information about how Private Sessions work—as well as more info regarding how you can permanently hide what you’re listening to, and how to make your personal playlists private (note that when you make a playlist private, nobody can access it, even if they have a link to it or search for it by name).
Bear in mind that if you’re using the web player, the Social settings won’t appear, as they can only be accessed from the desktop app at the moment; but if changed from the desktop app, these settings will apply to the web player and other devices you're logged in on as well.
If you’re using the desktop app and don’t see the options shown in my screenshot under Social, can you send a screenshot of how your Settings menu appears? You can include the screenshot in your next reply by using the “Insert Photos” option in the post editor. Make sure to hide sensitive information when posting on the Community.
I look forward to your reply, and let me know if you have any other questions.
Have a good day!
AdamDamonSpotify Star
Help others find this answer and click "Accept as Solution".
If you appreciate my answer, maybe give me a Like.
Note: I'm not a Spotify employee.