You shouldn’t need to touch any Login page as it’s completely out of your control.
The auth process involves sending the user to https://id.twitch.tv/oauth2/authorize with all the params for your app. If the user isn’t logged in to Twitch then that is handled on Twitch’s side of things as the user is on Twitch’s site, your app shouldn’t be interfering with that login process in any way.
When the user accepts/denies connecting their account to your app they’ll be redirected to your redirect url, and it’s at that point your app should complete the auth process. What happens between sending the user to Twitch, and them being redirected back to you, is completely out of your control.