## Why
`code_mode_only` moved ordinary runtime tools behind `exec`, but it also
hid hosted Responses tools. Hosted `web_search` and `image_generation`
do not have a nested `exec` runtime path, so code-only sessions lost
those capabilities entirely even when their existing provider, auth,
model, and configuration gates passed.
## What changed
- Keep hosted Responses tools top-level in `code_mode_only` sessions
after their existing gates pass.
- Preserve the existing nested-tool behavior for ordinary runtimes and
the direct-only behavior for multi-agent v2 tools.
- Add planner coverage for `code_mode_only` with default multi-agent v2
settings, hosted live web search, and hosted image generation.
## Verification
- Added focused regression coverage in
`codex-rs/core/src/tools/spec_plan_tests.rs`.
- Left execution to CI per repository workflow.
Ahmed Ibrahim
68e2c8ed69