Retry HTTP requests failing because of GitHub API SAML SSO enforcement with different token

[Gummibeer]

GitHub has an option for organizations to enforce SAML SSO for all API requests made to their organization by members.
https://docs.github.com/en/rest/overview/other-authentication-methods#authenticating-for-saml-sso

In case this happens the response is a 403 Forbidden with the following headers and body:

x-github-sso: required; url=https://github.com/orgs/stjude/sso?authorization_request=ABCXYZ

{
    "message":"Resource protected by organization SAML enforcement. You must grant your OAuth token access to this organization.",
    "documentation_url":"https://docs.github.com/articles/authenticating-to-a-github-organization-with-saml-single-sign-on/"
}

This has a massive impact on the queue right now they are catched by the rate-limit retry logic and do 12 requests over the duration of 12 hours to the API without any benefit/reason.
So far I know there's no attribute provided by API that indicates if an organization enforces SAML SSO. So the only way is to try'n'catch.
All these requests can pass and get a response if they are done with a non-member access-token. This works for us as we only request public data that wouldn't need an access-token at all. This problem is already reported to GitHub Support and is on their backlog/roadmap without any ETA.
As it prevents us right now from syncing two organizations:

• https://opendor.me/@Shopify
• https://opendor.me/@stjude

We have to solve it with a "temporary" fix. The idea is to detect this response the same as the rate-limit one and instead of just retrying it 1h later we would have to switch to a non-member access-token. So this will have to be solved in a Guzzle middleware.