I had been using a general Gmail to create a GCP account. However, in order to log onto GCP from a NextJS application via SAML, I applied for Cloud Identity through my GCP console. I created a Google Workspace account using a domain I own (example.com). After creating it, I logged into GCP using the ID from example.com (for example, admin@example.com) and set up the organization. After setting up SAML third-party authentication in Google Workspace, when logging into console.cloud.google.com, logging in with @example.com redirected me to a Third-Party SAML IdP, and I was able to log in.
What I want to know is,
In this case, is the GCP account originally used with Gmail completely different from the GCP account logged in with example.com?
Is it possible to set up SAML authentication for the GCP with the Gmail account?