Add a SessionStart hook (Claude parity) for pre-session script + context injection

What variant of Codex are you using?

CLI, Codex App, Cursor Codex

What feature would you like to see?

Add a first-class SessionStart hook, equivalent to Claude Code's SessionStart behavior.

I need a deterministic hook that runs once at session start (before the first user prompt is processed), so I can:

• run a local script
• gather project/runtime context
• inject that context into the session before normal turns continue

Why this matters

Current hooks are useful, but there is no explicit pre-session lifecycle point dedicated to one-time startup context hydration.

Without this, startup context workflows require wrappers/hacks and are not deterministic across session entry paths.

Proposed behavior

1. Add a new event, for example: SessionStart
2. Trigger exactly once per new session (not once per turn)
3. Trigger before first model turn/user-prompt processing
4. Make injection deterministic and explicit (e.g. additional context payload accepted by core)
5. Ensure consistent behavior across:

• codex interactive
• codex exec
• session resume/new-session paths (with clear policy)

Failure policy

Please make failure policy configurable, like other hooks:

• continue on hook error
• fail session start on hook error

Acceptance criteria

• A configured SessionStart hook runs once at the beginning of a session.
• Hook can return startup context that is injected before first turn.
• Startup behavior is deterministic and documented.
• Resume behavior is explicit (whether hook runs or not on resume).

Additional context

This is closely related to lifecycle hooks in #2109, but requesting an explicit dedicated pre-session hook with context injection semantics.