HttpServletStreamableServerTransportProvider seems not to work on subpath contextPath

[fabb]

Bug description
I want to run the HttpServletStreamableServerTransportProvider on a subpath of my jetty server, and have unrelated servlets on different contextPaths. Giving the ServletContextHandler of the MCP server a contextPath of a subpath (e.g. /mcp), makes the MCP server unreachable from the MCP Inspector.

Environment

• Version 0.11.0
• openjdk 24.0.1, the code runs as an extension in Bitwig Studio

Steps to reproduce

1. Create a Jetty server
2. Add a ServletContextHandler with a subpath "/mcp" as contextPath
3. Configure the HttpServletStreamableServerTransportProvider with mcpEndpoint "/" (or "/mcp", does not make a difference)
4. Add a servlet with this transport provider instance

Expected behavior

With the MCP Inspector (npx @modelcontextprotocol/inspector) it should be possible to connect to http://localhost:12345/mcp via Streamable HTTP.

When setting the contextPath to "/" and the transport's mcpEndpoint to "/mcp", the MCP Inspector can connect correctly and everything works. But I want to bind a different handler on "/" for serving a website.

Minimal Complete Reproducible example

        var jettyServer = new Server();

        ServerConnector connector = new ServerConnector(jettyServer);
        connector.setHost("localhost");
        connector.setPort("12345");
        jettyServer.addConnector(connector);

        var contextHandler = new ServletContextHandler();
        contextHandler.setContextPath("/mcp"); // using "/" would work correctly in combination with `.mcpEndpoint("/mcp")` - but I need a subpath as contextPath since I want to add another handler on the root path for serving a website
        jettyServer.setHandler(contextHandler);

        jettyServer.start();

        var objectMapper = new ObjectMapper();

        var transportProvider = HttpServletStreamableServerTransportProvider
            .builder()
            .objectMapper(objectMapper)
            .mcpEndpoint("/")
            .build();

        var mcpServer = McpServer.sync(this.transportProvider)
            .serverInfo("MyServer", "0.0.1")
            // ... register tools
            .build();

        contextHandler.addServlet(new ServletHolder(transportProvider), "/*");

[fabb]

Ok i think it‘s a jetty limitation, because jetty redirects /mcp to /mcp/ when defining a context path