Except HTTP prohibits copying headers from redirect responses to redirected requests. That's why OIDC exists, to deal with that by abusing URI q-params.

I've an Internet-Draft somewhere to fix this by making it possible to indicate on a 3xx that this is for authentication (so copy Authorization: from redirect responses to redirected requests) and to allow 401s to have Location: headers that make it more like a 3xx, and 3xxs have WWW-Authenticate:, so you can negotiate between legacy HTTP auth and redirect-based authentication.