Avoids unnecessary latency on the Settings page by restricting the
OAuth auth-status fallback to providers that are not in _PROVIDER_ENV_VAR.
Review feedback (PR #1221): the get_auth_status() call in the else branch
was firing for every unconfigured API-key provider (openai, anthropic, etc.),
adding a network round-trip per provider. Now it only runs for providers
that are not known API-key providers (custom/OAuth-capable providers).