I am not sure if I am understanding where the problem is occurring.
Are you using this library for DiscourseConnect: GitHub - spinen/laravel-discourse-sso: Integrate Discourse SSO into Laravel · GitHub?
Looking at that code (laravel-discourse-sso/src/Controllers/SsoController.php at develop · spinen/laravel-discourse-sso · GitHub), I am not how it is handling the case of a user who is already logged into the Laravel app.