Add native Vercel AI Gateway backend support

[jerilynzheng]

Summary

This PR adds native support for Vercel AI Gateway as a first-class backend, providing consistency with other gateway backends like OpenRouter.

Changes

• Backend Implementation: Added "vercel" to ClientBackend type and implemented in client factory with auto-configured base_url
• Documentation: Updated all documentation pages to showcase Vercel AI Gateway usage
• API Consistency: Uses creator/model-name format (e.g., openai/gpt-5.2, anthropic/claude-sonnet-4.5)

Usage

rlm = RLM(
    backend="vercel",
    backend_kwargs={
        "api_key": os.getenv("AI_GATEWAY_API_KEY"),
        "model_name": "openai/gpt-5.2",
    },
)

Testing

• ✅ Verified basic OpenAI model completion through Vercel
• ✅ Verified Anthropic model completion through Vercel
• ✅ Confirmed base_url auto-configuration
• ✅ Validated cost tracking works correctly

Benefits

• Simplified API - no manual base_url configuration needed
• Consistent with openrouter and vllm backends
• Access to multiple AI providers (OpenAI, Anthropic, Google, etc.) through one gateway

🤖 Generated with Claude Code