feat: add LiteLLM as AI gateway provider

[RheagalFire]

Summary

• Adds LiteLLM as a new LLM provider, enabling node-DeepResearch to route AI requests through 100+ LLM providers (OpenAI, Anthropic, Azure, Bedrock, Vertex AI, Groq, Cohere, Mistral, etc.) via a single LiteLLM proxy.
• Follows the existing provider pattern (same structure as OpenAI/Gemini providers).

Motivation

LiteLLM acts as a unified AI gateway. Instead of adding individual provider SDKs, users can set LLM_PROVIDER=litellm and point at a LiteLLM proxy that handles provider routing, load balancing, cost tracking, and fallbacks across 100+ providers. Useful for teams running centralized LLM infrastructure, or users who need providers not yet directly supported (e.g., AWS Bedrock, Cohere, Mistral).

Changes

• src/config.ts - added 'litellm' to LLMProvider type, added litellm case in getModel() using createOpenAI with configurable LITELLM_BASE_URL and LITELLM_API_KEY env vars, added env var exports
• config.json - added litellm provider entry and model configuration (mirrors openai config with openai/gpt-4o-mini as default model)

Tests

Live E2E - createOpenAI with LiteLLM proxy routing to Claude Sonnet 4.6:

Model: claude-sonnet-4-6
Content: OK
Finish: stop

This uses the exact same createOpenAI({ baseURL }) call path that getModel() uses when LLM_PROVIDER=litellm.

Risk / Compatibility

• Additive only. Existing openai/gemini/vertex providers untouched.
• No new dependencies - uses the existing @ai-sdk/openai package since LiteLLM proxy serves an OpenAI-compatible API.
• 2 files changed.

Example usage

# Set provider and proxy URL
export LLM_PROVIDER=litellm
export LITELLM_BASE_URL=http://localhost:4000/v1
export LITELLM_API_KEY=sk-your-key    # optional

# Start LiteLLM proxy
litellm --model anthropic/claude-3-5-sonnet --port 4000

# Run deep research as usual
npm start

Any LiteLLM model ID works in config.json:

"litellm": {
  "default": {
    "model": "openai/gpt-4o-mini"
  }
}

Programmatic usage (same API as existing providers):

import { getModel } from './src/config';

// Set LLM_PROVIDER=litellm in env, then:
const model = getModel('agent');  // resolves litellm config from config.json
// model is a standard Vercel AI SDK LanguageModel instance

// Or use directly:
import { createOpenAI } from '@ai-sdk/openai';
import { generateText } from 'ai';

const litellm = createOpenAI({
    apiKey: process.env.LITELLM_API_KEY,
    baseURL: process.env.LITELLM_BASE_URL || 'http://localhost:4000/v1',
});

const result = await generateText({
    model: litellm('anthropic/claude-3-5-sonnet'),
    prompt: 'What is deep research?',
});
console.log(result.text);

[RheagalFire]

cc @hanxiao