Move skill catalog rendering out of core (#36364)

## What changed

- Make the skills extension own the catalog prompt templates and rendering path.
- Remove the duplicate core fallback that injected available skills into initial context.
- Update core integration tests to install the skills extension explicitly when they expect model-visible skill context.

GitOrigin-RevId: bbe6b15c4e776a09c98b7f4166426fe4e58434ba

codex-rs/core/src/lib.rs

@@ -89,11 +89,9 @@ pub mod skills;
 pub(crate) use skills::SkillInjections;
 pub(crate) use skills::SkillMetadata;
 pub(crate) use skills::SkillsService;
-pub(crate) use skills::build_available_skills;
 pub(crate) use skills::build_skill_injections;
 pub(crate) use skills::build_skill_name_counts;
 pub(crate) use skills::collect_explicit_skill_mentions;
-pub(crate) use skills::default_skill_metadata_budget;
 pub(crate) use skills::injection;
 pub(crate) use skills::maybe_emit_implicit_skill_invocation;
 pub(crate) use skills::skills_load_input_from_config;