Are you using an Okta Classic org, or an Okta Identity Engine org?
What you’re describing sounds similar to a limitation in Okta Classic that, in a self-hosted widget, Federated Users (e.g. users from an external IdP like Google) will only be logged into Okta, but the /authorize request is not made (this is mentioned in the widget readme here).
If this is an Okta Classic org, there’s a solution for this outlined here: Social auth redirect not working with Okta Sign-In Widget | Okta Help Center