feat: add LiteLLM as LLM provider

[RheagalFire]

Summary

• Add LiteLLM as an alternative LLM provider alongside Ollama, giving MoneyPrinter users access to 100+ LLM providers (OpenAI, Anthropic, AWS Bedrock, Vertex AI, Groq, Cohere, Mistral, Together, Fireworks, etc.) through the LiteLLM Python SDK
• Activated by setting LLM_PROVIDER=litellm in .env
• Uses litellm.completion() with drop_params=True, provider API keys read from standard environment variables

Changes

• Backend/gpt.py -- add _litellm_generate_response() calling litellm.completion() with timeout and bounds checking; route via LLM_PROVIDER env var with validation; add _list_litellm_models() for model discovery; existing Ollama code untouched
• Backend/main.py -- update /api/models to use provider-aware list_models() with correct error messages per provider
• .env.example -- document LLM_PROVIDER, LITELLM_MODEL settings
• pyproject.toml -- add litellm>=1.80.0,<1.87.0 as optional dependency (pip install moneyprinter[litellm])

Tests

Live E2E (Azure Foundry -> Claude Sonnet 4.6, through actual gpt.generate_response() code path):

# From Backend/gpt.py -- _litellm_generate_response()
response = litellm.completion(
    model=model_name,
    messages=[{"role": "user", "content": prompt}],
    stream=False,
    drop_params=True,
    timeout=LITELLM_TIMEOUT,
)

Response: pong

Example usage

# .env
LLM_PROVIDER=litellm
LITELLM_MODEL=anthropic/claude-sonnet-4-20250514
ANTHROPIC_API_KEY=sk-ant-...

pip install moneyprinter[litellm]
uv run python Backend/main.py

Risk / Compatibility

• Additive only -- all existing Ollama code and behavior is untouched
• LLM_PROVIDER defaults to "ollama", preserving existing behavior; unknown values log a warning and fall back to Ollama
• litellm is an optional dependency -- existing users without it are unaffected (lazy import inside _litellm_generate_response)
• drop_params=True ensures unsupported params are silently dropped per provider
• Timeout matches existing Ollama timeout default (180s)
• list_ollama_models remains as alias for backward compatibility

[RheagalFire]

cc @FujiwaraChoki