feat(litellm): add support for local proxy without API key

[vinit13792]

Summary

• Add litellm to the interactive provider selection menu
• Support LITELLM_BASE_URL for local proxy deployments (no API key required)
• Auto-add openai/ prefix when using api_base for proper LiteLLM routing
• Add dummy API key for local proxies (OpenAI SDK requirement)
• Add validation and tests for litellm provider configuration

Changes

CLI (packages/cli)

• Added litellm to _PROVIDER_ENV and _PROVIDER_SIGNUP in ui.py
• Updated _detect_provider_status() to check for LITELLM_BASE_URL
• Updated interactive_provider_select() to skip API key prompt for local proxy
• Added litellm handling in helpers.py resolve_provider() and validate_provider_config()

Core (packages/core)

• Updated LiteLLMProvider to auto-add openai/ prefix when api_base is set
• Added dummy API key (sk-dummy) for local proxy without authentication

Tests

• Added 3 litellm validation tests in tests/unit/cli/test_helpers.py
• Created new tests/unit/test_providers/test_litellm_provider.py with 14 tests

Test Plan

• All existing tests pass
• New unit tests added and passing
• Manual testing with local litellm proxy at localhost:4000
• Code formatted with ruff

🤖 Generated with Claude Code

[RaghavChamadiya]

This is clean. The sk-dummy workaround is exactly what the LiteLLM docs recommend for local proxies, and the openai/ prefix auto-add is the right UX touch. 14 tests is solid coverage.

One small request before merge: add a comment next to the sk-dummy value so it does not trip future secret-scanning tools:

# LiteLLM requires a non-empty key even for unauthenticated local proxies (OpenAI SDK requirement)
call_kwargs["api_key"] = "sk-dummy"

This appears in two places in litellm.py (_generate_with_retry and stream_chat). Once that comment is added, I am ready to merge.

[vinit13792]

Yup makes sense! Updated! Ready for you to merge the code.