I use the Atlassian MCP server with tools like Claude code or Cursor. I often need to work across multiple Atlassian sites, but currently, it seems that the site (cloudId) selection is managed internally by the client and can’t be set or overridden per project in the mcp.json configuration.
Is there a way to specify the target Atlassian site (cloudId) per project or workspace in the MCP client configuration, without having to re-authenticate every time I switch projects?