## Summary
- allow the native Responses API `image_generation` tool when the active
provider carries CCA's non-empty `x-openai-actor-authorization` header
- preserve the Codex-managed ChatGPT auth path, scoped to providers that
actually require OpenAI auth
- keep generic custom providers excluded, including when unrelated
ChatGPT credentials are cached
- retain the existing feature, provider-capability, and
image-input-modality gates
## Why
CCA authenticates its inference requests through the active provider's
`x-openai-actor-authorization` and `ChatGPT-Account-ID` headers, so it
does not have a Codex-managed login session. The previous gate therefore
hid the native hosted image-generation tool despite an authenticated
codex-backend path.
This change is intentionally limited to the native hosted tool. It adds
no extension, MCP, plugin-service, session-source, token plumbing, or
new provider configuration surface.
## Tests
- `cargo test -p codex-core
hosted_tools_follow_provider_auth_model_and_config_gates`
- `cargo fmt --all -- --check`
- `git diff --check origin/main`
richardopenai
c660e2b644