How to convert a registry server.json into client configuration files (e.g. mcp.json, ~/.claude.json, .cursor/mcp.json)

Hi team 👋,

I'm trying to understand how to convert a registry server.json (from the MCP registry format) into the configuration format used by different MCP-compatible clients — for example:

VS Code / GitHub Copilot Chat: mcp.json

Claude Code: ~/.claude.json

Cursor: .cursor/mcp.json

Currently, the registry server.json defines fields.
However, it’s not immediately clear how these map to the client configuration structure (e.g. the "type", "command", "args", "env", "url", "headers" fields in client configs).

Could you clarify:

Is there an official or recommended mapping between the server.json schema and the client configuration schema?

Are there any tools or scripts (official or community-maintained) to automate this conversion?

For remote servers (e.g. using sse or websocket), how should authentication headers or environment variables be handled in client configs?

An example mapping between a sample server.json and equivalent mcp.json / ~/.claude.json / .cursor/mcp.json entries would be especially helpful 🙏

Thanks in advance for your guidance — this would make it much easier to integrate registry MCP servers into different clients!

Start by comparing the registry server.json fields with the mentioned VS Code/Copilot mcp.json, Claude Code ~/.claude.json, and Cursor .cursor/mcp.json formats. Document whether an official mapping or conversion tool exists, including the remote-server authentication cases; done means a sample mapping and guidance for each client are provided.