Add Anthropic Messages & OpenAI Responses API examples

[ericflo]

What

Adds integration examples for the two other API formats ModelRelay supports but weren't documented on the /integrate page.

Changes

• New Anthropic Messages API section (/v1/messages) with curl, Python SDK, and streaming examples
• New OpenAI Responses API section (/v1/responses) with curl, Python SDK, and streaming examples
• Response Formats section now shows all three API response shapes (Chat Completions, Messages, Responses) plus their SSE streaming formats
• Live Demo now has an API format dropdown to test Chat Completions, Messages, or Responses API
• Quick Reference updated to list all supported endpoints: /v1/chat/completions, /v1/messages, /v1/responses, /v1/models
• Reorganized "Languages & SDKs" and "Streaming" into a single "OpenAI Chat Completions" section with inline stream tabs

Why

ModelRelay proxies /v1/messages and /v1/responses alongside /v1/chat/completions (all confirmed in http.rs lines 96-98), but the integrate page only showed Chat Completions. Users had no way to discover the Anthropic or Responses API compatibility — a major selling point that was completely invisible.

Testing

• cargo build — clean
• cargo test — all pass
• cargo clippy — no warnings