allow_implicit_invocation: false also disables explicit $skill invocation, contradicting docs

Docs (https://developers.openai.com/codex/skills → learn.chatgpt.com/docs/build-skills) state that with agents/openai.yaml:

policy:
  allow_implicit_invocation: false

"the skill is not injected into the model context by default, but can still be invoked explicitly via $skill."

Measured on codex-cli 0.149.0 (macOS), the second half doesn't hold: $skill mentions of a policy-restricted skill are not expanded.

Repro:

1. Create ~/.codex/skills/test-policy/SKILL.md (name/description frontmatter, body marker POLICY-BODY) and agents/openai.yaml with the policy above.
2. Create ~/.codex/skills/test-plain/SKILL.md identically, no openai.yaml.
3. Run codex debug prompt-input '$test-plain go' → skill body is injected.
4. Run codex debug prompt-input '$test-policy go' → prompt contains only the literal text; no expansion, and the skill is absent from <skills_instructions>.

Same behavior through codex app-server threads. So a skill with the policy has no invocation path at all in non-TUI surfaces.

Expected: either $skill works for policy-restricted skills (docs behavior), or the docs state that allow_implicit_invocation: false disables explicit invocation outside the TUI picker.

Start with the codex debug prompt-input entry point and compare it with codex app-server thread handling using the provided test-policy and test-plain skill setup. Trace how $skill mentions and allow_implicit_invocation: false are handled; done means either explicit invocation expands the restricted skill or the behavior and documentation are aligned.