feat: add LiteLLM as AI gateway provider

[RheagalFire]

Summary

Adds LiteLLM as a third provider alongside DeepSeek and OpenRouter, giving users access to 100+ LLM providers (Anthropic, OpenAI, Bedrock, Vertex AI, Groq, etc.) through a single provider = "litellm" config change.

Motivation

The current provider system supports DeepSeek and OpenRouter. LiteLLM adds 100+ providers via its SDK without needing a separate proxy. Users set provider = "litellm" in config.toml, pick any model string (e.g. anthropic/claude-sonnet-4-6), and LiteLLM routes to the right provider using standard env vars (ANTHROPIC_API_KEY, OPENAI_API_KEY, etc.). drop_params=True handles cross-provider kwarg incompatibilities automatically.

Changes

• src/standard/llm_client.py -- added "litellm" to PROVIDER_DEFAULTS, new _litellm_chat_completions() function using litellm.completion() with drop_params=True, provider kwarg threaded through chat_completions()
• src/standard/llm_rewriter.py -- forwards provider kwarg
• src/standard/pipeline.py -- forwards provider kwarg to both rewrite steps
• src/methodologies/llm_rewriter.py -- forwards provider kwarg

Tests

Existing tests (12/12 pass):

tests/test_llm_client.py  12 passed in 0.02s

Live E2E (LiteLLM SDK -> Azure Foundry -> Claude Sonnet 4.6):

Response: '4'
=== E2E PASSED ===

Example usage

# config.toml
[llm]
provider = "litellm"
model = "anthropic/claude-sonnet-4-6"

# LiteLLM reads provider API keys from env vars
export ANTHROPIC_API_KEY="sk-ant-..."
python examples/example_usage.py

from src.standard.llm_client import resolve_llm_config, chat_completions

config = {
    "llm": {"provider": "litellm", "model": "anthropic/claude-sonnet-4-6"},
    "api_keys": {},  # litellm reads ANTHROPIC_API_KEY from env
}
llm = resolve_llm_config(config)

result = chat_completions(
    [{"role": "user", "content": "Rewrite this naturally: The experiment was conducted."}],
    api_key=llm["api_key"],
    base_url=llm["base_url"],
    model=llm["model"],
    temperature=llm["temperature"],
    provider=llm["provider"],
)
print(result)
# "We ran the experiment." (or similar humanized output)

Any LiteLLM-supported model string works: openai/gpt-4o, groq/llama-3.3-70b-versatile, deepseek/deepseek-chat, bedrock/anthropic.claude-v2, etc.

[RheagalFire]

cc @molly554