Move markInitialized/reconnect after status code check in Streamable HTTP transport

When the server returns a non-2xx status code (e.g. 405 Method Not Allowed),
markInitialized() and reconnect() were called before the status code was
checked. This caused an unnecessary GET request, which is problematic when
using transport fallback (Streamable HTTP -> SSE) as it creates duplicate
SSE sessions on the server.

Move markInitialized() and reconnect() inside the 2xx success branch so
they are only called when the server actually accepted the connection.

Fixes #773

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>

Author: rameshreddy-adutla

mcp-core/src/main/java/io/modelcontextprotocol/client/transport/HttpClientStreamableHttpTransport.java

@@ -478,19 +478,20 @@ public Mono<Void> sendMessage(McpSchema.JSONRPCMessage sentMessage) {
 					})).onErrorMap(CompletionException.class, t -> t.getCause()).onErrorComplete().subscribe();
 
 			})).flatMap(responseEvent -> {
-				if (transportSession.markInitialized(
-						responseEvent.responseInfo().headers().firstValue("mcp-session-id").orElseGet(() -> null))) {
-					// Once we have a session, we try to open an async stream for
-					// the server to send notifications and requests out-of-band.
-
-					reconnect(null).contextWrite(deliveredSink.contextView()).subscribe();
-				}
-
 				String sessionRepresentation = sessionIdOrPlaceholder(transportSession);
 
 				int statusCode = responseEvent.responseInfo().statusCode();
 
 				if (statusCode >= 200 && statusCode < 300) {
+					if (transportSession.markInitialized(responseEvent.responseInfo()
+						.headers()
+						.firstValue("mcp-session-id")
+						.orElseGet(() -> null))) {
+						// Once we have a session, we try to open an async stream
+						// for the server to send notifications and requests
+						// out-of-band.
+						reconnect(null).contextWrite(deliveredSink.contextView()).subscribe();
+					}
 
 					String contentType = responseEvent.responseInfo()
 						.headers()