Move installation ID resolution out of core startup (#21182)

## Summary

- resolve or inject the installation ID before core startup and pass it
through `ThreadManager`, `CodexSpawnArgs`, and `Session` as a plain
`String`
- keep child sessions on the parent installation ID instead of
rediscovering it inside core
- propagate installation ID startup failures in `mcp-server` instead of
panicking

## Why

Core was still touching the filesystem on the session startup path to
discover `installation_id`. This moves that work to the outer host
boundary so core no longer depends on `codex_home` reads during session
construction.

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Co-authored-by: Codex <noreply@openai.com>

codex-rs/core-api/src/lib.rs

@@ -42,6 +42,7 @@ pub use codex_core::config::ThreadStoreConfig;
 pub use codex_core::config::find_codex_home;
 pub use codex_core::init_state_db;
 pub use codex_core::init_state_db_from_config;
+pub use codex_core::resolve_installation_id;
 pub use codex_core::skills::SkillsManager;
 pub use codex_core::thread_store_from_config;
 pub use codex_exec_server::EnvironmentManager;