BetterClaude Gateway. Anthropic: /claude/{host}/v1/messages  OpenAI: /openai/{host}/v1/chat/completions or /openai/{host}/v1/responses  Gemini: /gemini/{host}/v1beta/models/{model}:generateContent  Vertex: /vertex/aiplatform.googleapis.com/v1/projects/{p}/locations/{loc}/publishers/google/models/{model}:streamGenerateContent