I think you are looking for IDP Single Logout. I have not tried this option. You can refer this documentation https://docs.aws.amazon.com/cognito/latest/developerguide/cognito-user-pools-managing-saml-idp-console.html for more details.
As per documentation, if the logout checkbox is enabled, it should work. Since it is a SAML logout, it might have to be triggered from browser.