gitLab integration for login for multiple team


We currently having one team configured to use gitlab for login into concourse (GitLab configured as OAuth2 authentication service provider).
We needed to create other teams using the same login method on the same concourse instance.
We configured each team accordingly.
Using the concourse graphical interface, we can see the new teams available and when we select Login we are redirected to gitLab successfully. But the flow is interrupted with an error “token verification failed”. It works from concourse to gitlab but then failed from gitlab to concourse in the way back.
We are wondering if it is a limitation from concourse, maybe problem around variable CONCOURSE_EXTERNAL_URL or the Callback URL.
We tried with 1 and with multiple applications on gitLab side but it leads to the same result (and the fact that they should be configured with the same callback url is the reason why we are maybe suspecting a limitation somewhere).

So we are not sure if we are missing some configurations somewhere or just facing a limitation.

Any feedback/help would be appreciated.