Stop re-exporting skill APIs from codex-core (#37984)

## What changed

- Import skill metadata and mention helpers directly from `codex-skills`.
- Import host skill loading types directly from `codex-skills-extension`.
- Make the remaining `codex-core` skills module private and remove its skill API re-exports, including the `HostSkillsService` re-export from `codex-core-api`.

GitOrigin-RevId: 26bf8fffd980df9c4d0c308d7e983ceab9a5df82

codex-rs/core/src/session/mod.rs

@@ -303,7 +303,6 @@ pub(crate) struct PreviousTurnSettings {
     pub(crate) realtime_active: Option<bool>,
 }
 
-use crate::HostSkillsService;
 use crate::exec_policy::ExecPolicyUpdateError;
 use crate::guardian::GuardianReviewOptions;
 use crate::guardian::GuardianReviewSessionManager;
@@ -384,6 +383,7 @@ use codex_protocol::protocol::TokenUsageInfo;
 use codex_protocol::protocol::TurnModerationMetadataEvent;
 use codex_protocol::protocol::WarningEvent;
 use codex_protocol::user_input::UserInput;
+use codex_skills_extension::HostSkillsService;
 use codex_tools::UnifiedExecShellMode;
 use codex_utils_absolute_path::AbsolutePathBuf;
 #[cfg(test)]