So far, I’m at the point where I discovered that omniauth-saml is the library used to manage SAML authentication. Studying the configuration of such library, helped me to perform a login succesfully, even if it was unclear to me, in the beginning, that the IDP target URL for login and logout have to be used as GET.
In any case, now omniauth.saml is logging errors (when they occurs).
So in the end, I guess that a summary of this thread could be: if there are no logs or evidence of SAML authentication in the logs, it is because the omniauth-saml is misconfigured or not invoked at all (due to idp problems).