Add hook support for IDE extension and Codex app

[Zeoy2020]

What variant of Codex are you using?

App, IDE Extension

What feature would you like to see?

Description:
Currently, Codex CLI supports hook functionality, which is very useful for customizing workflows and extending behavior. However, the IDE extension and Codex app do not yet support hooks. This creates an inconsistency across the ecosystem and limits developers who rely on the IDE or app for their daily work.

Impact:
Developers using the IDE extension or Codex app cannot leverage hooks for automation or customization.

This reduces adoption of hooks and fragments workflows between CLI and non-CLI environments.

Request:
Please add hook support to the IDE extension and Codex app, aligning them with the CLI implementation.

Additional information

No response

[etraut-openai]

The IDE Extension and App are built on the CLI. They are effectively a GUI wrapper on top of the CLI functionality. The hooks features are already supported.

[oxysoft]

Indexed this hook ticket in the umbrella tracker: #21753

Goal: collect the scattered Codex hook requests and bugs into one parity matrix for Full Claude Code Hook Parity (29+), while preserving this issue as the detailed thread for its specific behavior.