Make request cookies available to AuthManager methods

### Description

Add an interface for Auth Managers to access the request cookies from an auth request, in order to enable reading from the user's cookies at auth time.

### Use case/motivation

In order to separate out the JWTs for Keycloak and Airflow, we need to be able to retrieve the Keycloak JWT cookies from cookies inside the auth manager. To do this we currently need to either add the keycloak JWTs to the airflow JWT, which is sub-optimal because it creates a very large cookie, risking rejection on most browsers, or we need to modify the refresh token flow to also pass through a request object with the cookies included.

### Related issues

#70707

### Are you willing to submit a PR?

- [ ] Yes I am willing to submit a PR!

### Code of Conduct

- [x] I agree to follow this project's [Code of Conduct](https://github.com/apache/airflow/blob/main/CODE_OF_CONDUCT.md)

Start by tracing the auth request and the AuthManager methods involved, then review related issue #70707 for context. Done means auth managers can access request cookies during authentication, including the Keycloak JWT cookies, without enlarging the Airflow JWT or changing the refresh-token flow to pass a request object.

Written by the indexing model from the issue text.