The SAML assertion itself will be contained within a query parameter in the URL.

There is nothing inherent in SAML for passing other query parameters.

Within the SAML assertion, you can add additional SAML attributes, like an email address, and this is supported with Okta.

When performing an IdP-initiated login, Okta does not have functionality built in for adding additional query parameters like in the scenario you outlined.

I suspect you could add a static query parameter to the end of the SSO URL, but that wouldn't be a unique email address for every user.

If you're performing SP-initiated logins, I believe you can specify an index of SSO URL's and have the SAML response go to the typical SSO URL but with a different query parameter. This would only work for SP-initiated logins, would only work if the SP supported it, you'd still have to somehow have the SP specify the SSO URL in the index that has the corresponding email address, and the functionality was not built for this use case, so it would likely not scale and be difficult to manage.

You can also build a custom solution.

Maybe a feature request is in order.