`/side` can inherit an unexpected model, and `/model` is unavailable inside the side conversation

What version of Codex CLI is running?

codex-cli 0.130.0

What subscription do you have?

Pro

Which model were you using?

_No response_

What platform is your computer?

Darwin 25.4.0 arm64 arm

What terminal emulator and version are you using (if applicable)?

_No response_

What issue are you seeing?

/side can open a side conversation with a model that does not match the conversation I started it from, and then there is no way to correct it because /model is unavailable inside the side conversation.

What steps can reproduce the bug?

1. Start Conversation A using gpt-5.5.
2. Later, Conversation B and choose gpt-5.3-codex-spark.
3. Return to Conversation A.
4. Run /side.
5. Side Conversation A is limited to gpt-5.3-codex-spark.

What is the expected behavior?

• When the active conversation is a /side conversation, /model should open the model picker.
• The selected model should only apply to the active side conversation, and not change the parent conversation or global/default model.
• A side conversation should not unexpectedly inherit a newer global/default model from a different conversation.

Additional information

_No response_