Codex Quick Chat does not consistently receive live conversation updates from other clients

What version of the Codex App are you using (From “About Codex” dialog)?

Version 26.715.31925

What subscription do you have?

Plus

What platform is your computer?

macOS

Environment

Same OpenAI account
Same conversation opened simultaneously
ChatGPT Classic (macOS)
ChatGPT Codex App – Quick Chat (macOS)

What issue are you seeing?

I observed inconsistent live synchronization when the same conversation is open simultaneously in ChatGPT Classic and Codex Quick Chat.

Steps to reproduce
Open the same conversation in ChatGPT Classic and Codex Quick Chat.
Send a message from Classic.
Observe the Quick Chat window.

Observed behavior
Messages sent from Classic do not consistently appear live in Quick Chat.
Assistant responses generated after those messages may also fail to appear immediately in Quick Chat.
In contrast, messages sent from Codex appear in Classic after approximately 1–2 seconds.
Refreshing or otherwise reactivating Quick Chat appears to synchronize the conversation.

Expected behavior
Both clients should receive live conversation updates while the conversation is open.

Additional observations
The issue appears to be specific to Codex Quick Chat.
ChatGPT Classic receives updates normally with only a short synchronization delay (around 1–2 seconds).

What steps can reproduce the bug?

Open the same conversation in ChatGPT Classic and Codex Quick Chat.
Keep both windows open side by side.
In ChatGPT Classic, send a new user message.
Observe Codex Quick Chat for at least 10–15 seconds.
Optionally, let the assistant reply in Classic and continue observing Quick Chat.

What is the expected behavior?

The new user message appears automatically in Codex Quick Chat.
The assistant's reply also appears automatically without any user interaction.

Actual result
The new user message does not appear in Codex Quick Chat.
The assistant's reply also does not appear live.
The conversation only updates after Quick Chat is refreshed or otherwise reactivated.

Additional information

The opposite direction behaves differently: messages sent from Codex appear in ChatGPT Classic after approximately 1–2 seconds, suggesting the issue is specific to Quick Chat rather than the conversation backend.