Add Daybreak models to Codex agent settings and persist the chosen model on relaunch

When creating or editing a saved agent with Codex as its provider, the user reports that Daybreak models are missing from AgentsRoom's Model picker. They can select a Daybreak model manually using /model inside Codex, but after restarting or relaunching the agent, the console returns to its configured/default model and they must repeat the manual selection.

Steps reported by the user:

1. Create or edit a saved agent and select Codex.
2. Open the Model picker: Daybreak cannot be selected.
3. Start the agent and select Daybreak through Codex's /model.
4. Restart or relaunch the agent: the manual selection must be repeated.

Read-only verification: the local Codex model catalog lists Daybreak Blue as gpt-daybreak-blue-latest, with visibility set to list. The picker/relaunch behavior has not been independently reproduced.

Official identifiers to consider:

• Daybreak Blue: gpt-daybreak-blue-latest
• Daybreak Red: gpt-daybreak-red-latest
• Documented Daybreak Red model: gpt-5.6-cyber

Only Blue was confirmed in this session's Codex catalog. Red availability depends on account access and Codex support.

Proposal: expose Daybreak models available to the current Codex account in the Add/Edit agent picker, save the selected model in the agent configuration, and reuse it when restarting, relaunching or resuming that agent.

Expected outcome: configure the model once without repeating /model after each relaunch.

Official model reference: https://developers.openai.com/api/docs/guides/daybreak