Seems like you didn't mentioned whihc entity you need to consider for the uniqueness
When debugging the login of a SAML you need to do a couple of things. First make sure that you set the lognode for SAML to trace. Otherwise you only get generic logs that does not tell you the real problem. Second thing is that you need to inspect in the SAML module the xml files. One is the request to the IdP and the other is the response from the IdP.
And you could use SAML tracer a firefox plugin to debug the SSO. It will give you detailed information where it might have gone wrong. From the current fault it seems that you did not do all the steps of the configuration wizard.
And do note that on 28-5-2021 a new version of the SAML module was released. I would update if I where you.