It's good to know that you've already taken some steps. However, it's better to open the password reset form in a private/incognito window, and choose a strong password you haven't used before.
Then you can go to your account page and click SIGN OUT EVERYWHERE again.
It's also strongly advised that you change the password for:
- The email address associated with your Spotify account (e.g. with Gmail, Hotmail, etc.).
- Any Facebook profile associated with your Spotify account. You can make sure you're the only one currently logged into your Facebook in your Facebook Settings, under Security and login > Where You’re Logged In.
- Any service where you use the same password as Spotify.
Make sure to check this article as well, in order to protect your Spotify account.
If the issue persists, you can reach out to Customer Support.
You can find the contact form here.
I hope it helps!
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Note: I'm not a Spotify employee.