Not sure what curl has to do with it…
Step One of the oAuth is a redirect to Twitch, which is not performed via cURL. Just answered this one your other thread at
https://discuss.dev.twitch.com/t/is-possile-change-the-redirect-name-generated-by-the-api/18942/8
I don’t think you understand how oAuth operates clearly enough.
You the application creator have zero control over Twitch session management as that is handled by the Twitch website, so no, your server/application/website, cannot log the user out of another website.