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-skills/src/lib.rs

@@ -5,7 +5,6 @@ pub mod loader;
 mod mention_counts;
 pub mod model;
 pub mod remote;
-pub mod render;
 mod root_loader;
 pub mod service;
 mod skill_instructions;
@@ -20,15 +19,6 @@ pub use model::SkillLoadOutcome;
 pub use model::SkillMetadata;
 pub use model::SkillPolicy;
 pub use model::filter_skill_load_outcome_for_product;
-pub use render::AvailableSkills;
-pub use render::SKILLS_HOW_TO_USE_WITH_ABSOLUTE_PATHS;
-pub use render::SKILLS_HOW_TO_USE_WITH_ALIASES;
-pub use render::SKILLS_INTRO_WITH_ABSOLUTE_PATHS;
-pub use render::SkillMetadataBudget;
-pub use render::SkillRenderReport;
-pub use render::build_available_skills;
-pub use render::default_skill_metadata_budget;
-pub use render::render_available_skills_body;
 pub use root_loader::PluginSkillSnapshots;
 pub use service::SkillsLoadInput;
 pub use service::SkillsService;