Handle the same URL with Spring MVC RequestMapping

What do I want to have:

Client sends GET / HTTP/1.1(without Connection: upgrade) - this request should be handled by RequestMappingHandlerMapping
Client sends Connection: upgrade along with GET request - this request should be handled by ServletWebSocketHandlerRegistry

My Java configuration:

@Configuration
@EnableWebSocket
public class WebsocketConfiguration extends WebMvcConfigurationSupport 
                                    implements WebSocketConfigurer {
    @Bean
    WebsocketComponent wsHandler() {
        return new WebsocketComponent();
    }

    @Override
    public void registerWebSocketHandlers(WebSocketHandlerRegistry registry) {
        registry.addHandler(wsHandler(), "/").setAllowedOrigins("*");
    }
}

My webmvc controller:

@Controller
public class Status {
    @RequestMapping(value = "/", method = RequestMethod.GET)
    public String status() {
        return "OK";
    }
}

The problem is - when MVC controller taking precedence, it always respond with HTTP 200, WebSocket handler never reached. When WebSocket handler have precedence - it works with WebSocket client, but when I try http client(browser) it responds with Can "Upgrade" only to "WebSocket". Is it possible to replace somehow this error page with fallback to my MVC mapping? Any other configurations to make what I described first?

The problem is - when MVC controller taking precedence, it always respond with HTTP 200, WebSocket handler never reached

When RequestMappingHandlerMapping takes precedence over WebSocketHandlerMapping, for a request to an endpoint that both of them can handle (If you just consider the URL), DispatcherServlet would dispatch the request to @RequestMapping methods, not the WebSocket handler. In order to solve this problem, restrict @RequestMapping method to just serve the request without Connection:Upgrade header:

@Controller
public class Status {
    @RequestMapping(value = "/", method = GET, headers = "Connection!=Upgrade")
    public String status() {
        return "OK";
    }
}

This way, when DispatcherServlet searches for a handler for that common endpoint, it would consider the presence or absence of the Connection:Upgrade header to determine the right handler to fulfill the request.