fix: use JSON-RPC error format for session not found response

Format the 404 response body as a proper JSON-RPC error for
consistency with other transport error responses.

Github-Issue: #1727

Author: max-rousseau

src/mcp/server/streamable_http_manager.py

@@ -3,6 +3,7 @@
 from __future__ import annotations
 
 import contextlib
+import json
 import logging
 from collections.abc import AsyncIterator
 from http import HTTPStatus
@@ -288,9 +289,17 @@ async def run_server(
                 await http_transport.handle_request(scope, receive, send)
         else:  # pragma: no cover
             # Unknown or expired session ID - return 404 per MCP spec
-            # This tells the client to reinitialize
+            # Use JSON-RPC error format for consistency with transport errors
+            error_body = json.dumps(
+                {
+                    "jsonrpc": "2.0",
+                    "id": "server-error",
+                    "error": {"code": -32600, "message": "Session not found"},
+                }
+            )
             response = Response(
-                "Session not found",
+                content=error_body,
                 status_code=HTTPStatus.NOT_FOUND,
+                media_type="application/json",
             )
             await response(scope, receive, send)