MockRestServiceServer does not involve error handler annotated with @RestControllerAdvice

I am trying to write integration test in Spring Boot 2.7.3. This application should scrape data from some external REST service. To call rest service I am using RestTemplate from spring framework

@Service
public class UserService {
    private final RestTemplate restTemplate;

    private String url = "http://localhost:3000/user/{name}";

    @Autowired
    public UserService(RestTemplate restTemplate) {
        this.restTemplate = restTemplate;
    }

    public UserData getUserInfo(UserInfo userInfo) {
        return restTemplate.getForObject(url, UserData.class, userInfo.getName());
    }
}

This service is used by rest controller that is accepting name as a path parameter (we can call it localhost:8080/info?name=joe)

@RestController
public class UserController {

    private UserService userService;

    @Autowired
    public UserController(UserService userService) {
        this.userService = userService;
    }

    @GetMapping("/info")
    @ResponseBody
    public UserData getUserData(UserInfo userInfo) {
        return userService.getUserInfo(userInfo);
    }
}

I have created controller annotated with @RestControllerAdvice and handling method that should be invoked when throwing HttpClientErrorException

@RestControllerAdvice
public class UserExceptionHandler {

    @Autowired
    public UserExceptionHandler(){
    }

    @ExceptionHandler(value = {HttpClientErrorException.class})
    public ErrorResponse clientErrorHandle(HttpClientErrorException e) {
        return ErrorResponse.builder().error("could not retrieve user info").build();
    }
}

Problem is that below test is not hitting UserExceptionHandler

@SpringBootTest(webEnvironment = SpringBootTest.WebEnvironment.RANDOM_PORT)
class UserControllerTest {
    @Autowired
    RestTemplate restTemplate;

    @Autowired
    UserController userController;

    private MockRestServiceServer mockServer;

    @BeforeEach
    public void setUp() {
        mockServer = MockRestServiceServer.createServer(restTemplate);
    }
    @Test
    public void testGetRootResourceOnce() {
        mockServer.expect(once(), requestTo("http://localhost:3000/user/joe"))
                .andRespond(withBadRequest().contentType(MediaType.APPLICATION_JSON).body("{\"error\": \"Error while getting data\"}"));

        UserInfo userInfo = UserInfo.builder().name("joe").build();

        UserData userData = userController.getUserData(userInfo);

        mockServer.verify();
        assertThat(userData).isNotNull();
    }
}

While debugging I set breakpoint on UserExceptionHandler constructor so I assume that it has been created.

But why method clientErrorHandle was not invoked?

I see that RestTemplate throw HttpClientErrorException (please see picture below) so it should be intercepted by my handler, but it was not