ci: make public-hygiene-lint green - #2

busbar 1.5.3 retired two config surfaces this fixture still used: `auth.methods:`
and INLINE module entries under `auth.admin_auth:`. An identity provider is now
defined ONCE under `identity-providers:` -- `browser_login` and `settings`
hanging off that single definition -- and referenced elsewhere by bare name.

A config still carrying the old shape is not merely deprecated: core recognises
it as a 1.x config and refuses to start, so the fixture described a gateway that
could never come up. All the test could report was the symptom, a long way from
the cause:

  test github_*_flow ... FAILED
  panicked at tests/e2e.rs: busbar exited early during health poll: exit status: 1

Reproduced by rendering this fixture's own YAML and feeding it to a `busbar`
built from the core branch CI tests against:

  [error] config.yaml: this looks like a busbar 1.x config; run
          `busbar --migrate-config <config.yaml>` and review the flagged items.
          1.x markers found:
    - `auth.methods:` (retired 1.5.3 -> the matching `identity-providers:`
      definition (browser_login + settings are per-provider))
    - `auth.admin_auth:` carries INLINE module entries (retired 1.5.3 -> define
      the provider once under `identity-providers:` and reference it by bare name)

The replacement shape is core's own `--migrate-config` output for the previous
fixture, confirmed by re-validating: the 1.x gate is cleared and the only
remaining complaint is that the github plugin is not in the plugins directory,
which is precisely what this test puts there.