The legacy API framework allowed to pass the `run_as` user in the payload but, moving forward to the new framework, looks like the headers is a better place for it (see https://github.com/galaxyproject/galaxy/pull/11342/commits/91e7d5191d70f3b286fdf86b39af657bede35f09).
- Adapt existing framework tests to pass in the `run_as` user in the headers instead of the payload.
- Fix the legacy framework not retrieving the `run_as` from the headers when the payload was not in JSON (i.e. Form data)
- Add a bit more of documentation for the OpenAPI schema.