The logout functionality you’ve mentioned here is the default behavior of a module. It’s logging you out of Drupal but not from your Application/Provider.
To allow the module to logout from your provider/application account (what you are looking for), you need to make the below configurations:
- Go to the Sign In Settings tab.
- Add your provider’s Logout URL in the text field of the Default Redirect URL after logout.
- Click on the Save Configuration button.
Note: You will get this logout URL from your Provider/Application support.
If your Provider is Azure AD B2C, then you can find the solution by clicking this link.