BYOK: Support multiple external models/providers #4976

Describe the feature or problem you'd like to solve

The GitHub Copilot app supports configuring multiple external models/providers, while Copilot CLI currently supports only a single BYOK provider/model configuration.

Proposed solution

Extend the current configuration:
COPILOT_PROVIDER_BASE_URL
COPILOT_PROVIDER_API_KEY
COPILOT_MODEL
to support multiple provider/model profiles and allow switching between them.
The goal is to make Copilot CLI usable as a single agent harness across multiple model providers.

Example prompts or workflows

No response

Additional context

Some organizations require model/provider independence and therefore prefer a model-agnostic harness rather than provider-specific tools such as Codex or Claude Code.

Copilot CLI is a strong candidate for this role and competes with multi-provider tools such as OpenCode. However, supporting multiple configured providers is important for organizations adopting Copilot CLI strategically.

In our case, this capability would help justify Copilot CLI as a long-term, provider-independent solution; without it, we would likely need to consider replacing it with a multi-provider alternative.