feat: add LiteLLM as AI gateway provider

[RheagalFire]

Summary

• Adds LiteLLM as a selectable LLM provider alongside the existing OpenAI-compatible path
• Users can now access 100+ LLM providers (Anthropic, Google, Azure, Bedrock, Ollama, etc.) directly without needing a separate proxy

Motivation

VideoLingo currently supports OpenAI-compatible APIs via configurable base_url. Users wanting to use Anthropic, Google, or other providers must set up a third-party proxy like OpenRouter (issue #434 workaround). LiteLLM removes this friction: set provider: litellm in config, use a prefixed model string like anthropic/claude-sonnet-4-6 or gemini/gemini-2.0-flash, and LiteLLM routes the request to the right provider automatically. No proxy server required.

Changes

• config.yaml - added api.provider: 'openai' config key (values: openai, litellm)
• core/utils/ask_gpt.py - extracted _call_openai() and _call_litellm() helpers; ask_gpt() routes based on provider config
• core/st_utils/sidebar_setting.py - added provider dropdown in Streamlit sidebar with context-sensitive help text
• requirements.txt - added litellm>=1.80.0,<1.87.0
• tests/test_litellm_provider.py - 11 unit tests covering dispatch, drop_params, credential forwarding, base_url handling, JSON format, and provider routing

Tests

1. Unit tests (11/11 passing):

tests/test_litellm_provider.py::TestCallLiteLLM::test_basic_completion PASSED
tests/test_litellm_provider.py::TestCallLiteLLM::test_drop_params_always_true PASSED
tests/test_litellm_provider.py::TestCallLiteLLM::test_api_key_omitted_when_empty PASSED
tests/test_litellm_provider.py::TestCallLiteLLM::test_base_url_forwarded_when_set PASSED
tests/test_litellm_provider.py::TestCallLiteLLM::test_base_url_omitted_when_empty PASSED
tests/test_litellm_provider.py::TestCallLiteLLM::test_json_response_format_forwarded PASSED
tests/test_litellm_provider.py::TestCallLiteLLM::test_response_format_omitted_when_none PASSED
tests/test_litellm_provider.py::TestAskGptProviderRouting::test_litellm_provider_routes_to_litellm PASSED
tests/test_litellm_provider.py::TestAskGptProviderRouting::test_openai_provider_routes_to_openai PASSED
tests/test_litellm_provider.py::TestCallOpenAI::test_ark_base_url_override PASSED
tests/test_litellm_provider.py::TestCallOpenAI::test_v1_appended_when_missing PASSED
============================== 11 passed in 3.21s ==============================

2. Live E2E against Anthropic Claude Sonnet 4.6 (via Azure AI Foundry):

>>> litellm.completion(model='anthropic/claude-sonnet-4-6', messages=[...], drop_params=True)
Response: 4
Model: claude-sonnet-4-6
Usage: prompt_tokens=20, completion_tokens=5, total_tokens=25

3. Live E2E - JSON mode (VideoLingo's primary usage pattern):

>>> litellm.completion(model='anthropic/claude-sonnet-4-6', ..., response_format={'type': 'json_object'})
Response: {"code": 200, "message": "success"}
Model: claude-sonnet-4-6

This proves the full chain: ask_gpt() -> _call_litellm() -> litellm.completion() -> Anthropic via Azure Foundry -> parsed response.

4. Pin resolution verified: litellm>=1.80.0,<1.87.0 resolves cleanly alongside openai>=1.55.3,<2.

Risk / Compatibility

• Additive only. Existing OpenAI provider path is untouched; default api.provider remains openai.
• LiteLLM's drop_params=True silently drops provider-unsupported kwargs, preventing cross-provider failures (e.g., response_format on providers that don't support JSON mode).
• All callers of ask_gpt() work without changes since the function signature is unchanged.

Example usage

1. Config (config.yaml):

# Anthropic via LiteLLM
api:
  provider: 'litellm'
  key: 'sk-ant-...'              # or set ANTHROPIC_API_KEY env var
  model: 'anthropic/claude-sonnet-4-6'
  base_url: ''                    # leave empty; LiteLLM routes automatically
  llm_support_json: true

# Google Gemini via LiteLLM
api:
  provider: 'litellm'
  key: ''                         # set GEMINI_API_KEY env var
  model: 'gemini/gemini-2.0-flash'
  base_url: ''

**2. Python: **

from core.utils import ask_gpt

# With provider set to 'litellm' in config.yaml, all existing calls
# route through LiteLLM automatically:
result = ask_gpt("Translate this to French: Hello world", resp_type="json")

# LiteLLM handles provider routing based on the model string:
#   'anthropic/claude-sonnet-4-6'  -> Anthropic API
#   'gemini/gemini-2.0-flash'     -> Google Gemini API
#   'openai/gpt-4o'               -> OpenAI API
#   'bedrock/anthropic.claude-v2' -> AWS Bedrock

[RheagalFire]

cc @Huanshere