Fixes servlet transport error serialization so servlet transports write JSON-RPC error responses for McpError instead of serializing the Java exception object.

Fixes #955

Motivation and Context

Some servlet transport error paths currently serialize McpError directly. Since McpError extends RuntimeException, the response body can include exception-shaped fields such as stackTrace, cause, localizedMessage, and jsonRpcError.

This makes servlet error responses inconsistent with the JSON-RPC error response shape expected by MCP clients.

Before:

After:

How Has This Been Tested?

Added servlet transport tests covering JSON-RPC error serialization for:

• stateless servlet transport errors
• streamable servlet transport errors
• SSE servlet transport errors
• parsed request id preservation
• no-id transport-level rejection paths

I also verified the behavior locally with a small servlet server and Postman using the same request before and after the fix.

Breaking Changes

None intended.

The existing HTTP status behavior for transport-level rejections is preserved. The response body is changed to the expected JSON-RPC error envelope instead of serializing the McpError exception object.

Types of changes

• Bug fix (non-breaking change which fixes an issue)
• New feature (non-breaking change which adds functionality)
• Breaking change (fix or feature that would cause existing functionality to change)
• Documentation update

Checklist

• I have read the MCP Documentation
• My code follows the repository's style guidelines
• New and existing tests pass locally
• I have added appropriate error handling
• I have added or updated documentation as needed

Additional context

This change keeps the existing servlet transport status-code behavior for transport-level rejections, but writes a JSON-RPC error response body consistently.

When the request id has already been parsed, the response preserves it. For transport-level rejection paths where no request id is available, the response omits the id field.

References:

• MCP JSONRPCErrorResponse schema models error responses with jsonrpc, optional id, and error: https://modelcontextprotocol.io/specification/2025-11-25/schema#jsonrpcerrorresponse