Automations: automation created via chat may select unavailable model causing run failure

- Copilot Chat Extension Version:
- VS Code Version:
- OS Version:
- Feature: Automations (creating automations via chat / agent)
- Selected model: model chosen by the agent at creation time (not available on the agent host)
- Logs: Automation never runs; failure occurs when the agent host reports the selected model is unavailable. Related discussion: https://github.com/microsoft/vscode/issues/330701

Steps to Reproduce:
1. Create an automation using the chat/agent UI (chat-created automation).
2. The agent selects a model for the automation during creation.
3. The automation is saved but the selected model is not available on the agent host that runs automations.
4. Attempt to run the automation — it fails to start because the model cannot be found on the host.

Expected behavior:
- Either the chat/agent should only allow selecting models that will be available on the target agent host, or the automation should record a fallback/compatible model and/or surface a clear warning during creation.

Actual behavior:
- The agent can pick a model at creation that is not present on the agent host, causing the automation to fail to run later.

Additional context:
- Reported in internal discussion; appears related to how model pickers are populated by different chat input widgets and sessions. See related issue: https://github.com/microsoft/vscode/issues/330701

[View original Slack conversation](https://vscodeteam.slack.com/archives/C0AKR94N3CK/p1786748458571289?thread_ts=1786748458.571289&cid=C0AKR94N3CK)