External model provider fails in Chat mode with CAPIError 404

### Short summary

Using an external/custom model provider in Chat mode (not Projects mode) fails with a CAPIError: 404 response.

### Affected version or release

v1.0.10

### Installation context

The app is installed locally. The issue occurs when using Chat mode with an external/custom model provider configured.

### What happened?

When I use an alternative model provider and open a normal Chat session (outside of Projects mode), the request fails.

The same provider configuration may work in other contexts, but Chat mode returns an API error instead of sending the request to the configured provider.

### Steps to reproduce

- Open GitHub Copilot Desktop.
- Configure an external/custom model provider.
- Select the external provider as the active model.
- Open Chat mode (not Projects mode).
- Send a message.
- Observe that the request fails with a CAPI 404 error.

### Expected behavior

The Chat mode should use the configured external model provider and successfully send requests through that provider.

### Actual behavior

The request fails with:

- Execution failed: CAPIError: 404 404 status code (no body)
-
- The external model provider does not respond successfully in Chat mode.

### Additional context

Screenshot attached showing the error:

This appears to be related to external provider routing in Chat mode, where the request may still be going through Copilot's API layer instead of the configured provider endpoint.