Is it reasonable, If we use popup mode for Single Sign On?

Our applications have OAuth for Google and we use popup mode. The Login page has a button for authorization via Google.

But now customers want to use a single sign-on (SSO) for authentication. As I know about SSO, we haven't used a login page app, we redirect to the login page of the SSO website. So it makes sense when we use popup mode for SSO.

We put a button keycloak (SSO) and show a popup for authorization. But it's flow is the same OAuth.

Would you show me the reasonable way to use popup mode for SSO or SSO only use redirect mode?