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/session.rs

@@ -7,7 +7,6 @@ use crate::environment_selection::ThreadEnvironments;
 use crate::environment_selection::TurnEnvironmentSnapshot;
 use crate::session::turn_context::TurnEnvironmentConfig;
 use crate::shell_snapshot::ShellSnapshot;
-use crate::skills::SkillError;
 use crate::state::ActiveTurn;
 use codex_extension_api::ExtensionDataInit;
 use codex_http_client::ClientRouteClass;
@@ -26,6 +25,7 @@ use codex_protocol::protocol::MultiAgentVersion;
 use codex_protocol::protocol::ThreadHistoryMode;
 use codex_protocol::protocol::ThreadSource;
 use codex_protocol::protocol::TurnEnvironmentSelections;
+use codex_skills::SkillError;
 use std::sync::OnceLock;
 use tokio::sync::Semaphore;