Feature Request: Add support for Anthropic's Claude API

Nobody has claimed this yet.

First, thank you for creating such an amazing and indispensable tool for working with local LLMs.

The OpenAI-compatible server is one of its most powerful features, allowing a vast ecosystem of tools and applications to work seamlessly with local models.

I would like to propose a similar feature: **adding an Anthropic Claude-compatible API endpoint to the local server.**

**The Goal:**

The idea is to have the local server expose an endpoint that mimics the official Anthropic Claude Messages API. This would mean that any tool, library, or application built to communicate with the Claude API (e.g., using Anthropic's official SDKs) could be pointed to the LM Studio server and work out-of-the-box with any model running locally.

**Why this would be a great addition:**

1. **Seamless Integration:** It would allow developers to use the same codebase and tools for both the official Claude API and local models served by LM Studio, simply by changing the API base URL.
2. **Expanded Ecosystem:** This would significantly expand the interoperability of LM Studio, making it compatible with the growing ecosystem of applications being built specifically for the Claude API standard.
3. **Enhanced Workflow:** Just as the OpenAI compatibility has been a game-changer for development and testing, adding Claude compatibility would provide the same massive workflow benefits for another major API format.

Thank you for your hard work and for considering this feature request! It would be a fantastic enhancement.

The issue names no files, tests, or entry points. Start by locating the existing OpenAI-compatible server behavior mentioned in the request, then define the Claude Messages API compatibility scope; done means local models can be accessed through a compatible endpoint by Claude API tools and SDKs.

Written by the indexing model from the issue text.