Improve bridge dispatch and Codex app-server handshake

[axeldelafosse]

Summary

• extract shared bridge dispatch and guidance helpers
• validate Claude bridge replies against the active bridge chat id
• send initialized after initialize for Codex App Server clients and bridge injections
• opt bridge injections out of unused Codex App Server notifications
• add regression coverage for stale tmux delivery status and bridge/app-server handshake behavior

Verification

• bun run check
• bun test
• bun run build

[gemini-code-assist]

Code Review

This pull request refactors the bridge messaging system by modularizing dispatch logic and agent guidance into dedicated files. It also enhances the Codex app server integration by implementing a formal initialization handshake and allowing for notification method opt-outs. A validation check for the active bridge conversation was added to the reply tool. Feedback suggests exporting the notification opt-out constant to improve test maintainability.

[gemini-code-assist]

To improve test maintainability and avoid hardcoding values, consider exporting BRIDGE_OPT_OUT_NOTIFICATION_METHODS. This would allow the test file (tests/loop/codex-app-server.test.ts) to import and use this constant directly, making the tests less brittle to future changes in these notification methods.

Suggested change

	const BRIDGE_OPT_OUT_NOTIFICATION_METHODS = [
	METHOD_ERROR,
	METHOD_ITEM_COMPLETED,
	METHOD_ITEM_DELTA,
	METHOD_TURN_COMPLETED,
	METHOD_TURN_STARTED,
	] as const;
	export const BRIDGE_OPT_OUT_NOTIFICATION_METHODS = [
	METHOD_ERROR,
	METHOD_ITEM_COMPLETED,
	METHOD_ITEM_DELTA,
	METHOD_TURN_COMPLETED,
	METHOD_TURN_STARTED,
	] as const;