refactor(server): Fi StdioServerTransportProvider initialization flow (#74)

Extract message processing initialization from StdioMcpSessionTransport constructor into a
separate initProcessing() method.

Signed-off-by: Christian Tzolov <[email protected]>

Author: tzolov

mcp/src/main/java/io/modelcontextprotocol/server/transport/StdioServerTransportProvider.java

@@ -93,7 +93,9 @@ public StdioServerTransportProvider(ObjectMapper objectMapper, InputStream input
 	@Override
 	public void setSessionFactory(McpServerSession.Factory sessionFactory) {
 		// Create a single session for the stdio connection
-		this.session = sessionFactory.create(new StdioMcpSessionTransport());
+		var transport = new StdioMcpSessionTransport();
+		this.session = sessionFactory.create(transport);
+		transport.initProcessing();
 	}
 
 	@Override
@@ -142,10 +144,6 @@ public StdioMcpSessionTransport() {
 					"stdio-inbound");
 			this.outboundScheduler = Schedulers.fromExecutorService(Executors.newSingleThreadExecutor(),
 					"stdio-outbound");
-
-			handleIncomingMessages();
-			startInboundProcessing();
-			startOutboundProcessing();
 		}
 
 		@Override
@@ -181,6 +179,12 @@ public void close() {
 			logger.debug("Session transport closed");
 		}
 
+		private void initProcessing() {
+			handleIncomingMessages();
+			startInboundProcessing();
+			startOutboundProcessing();
+		}
+
 		private void handleIncomingMessages() {
 			this.inboundSink.asFlux().flatMap(message -> session.handle(message)).doOnTerminate(() -> {
 				// The outbound processing will dispose its scheduler upon completion