redis transaction alongside jdbc transaction

In our application we are using both MySQL server and Redis databases. we use Redis as a database and not just a cache. we use both of them in a service method and I want to make the method @Transactional to let the spring manages my transactions. Hence if in the middle of an transactional method a RuntimeException is thrown all works on both Redis and MySQL are rolled back. I have followed the spring docs and configured my @SpringBootApplication class as following:

@SpringBootApplication@EnableTransactionManagementpublic class TransactionsApplication {    @Autowired    DataSource dataSource;    public static void main(String[] args) {        SpringApplication.run(TransactionsApplication.class, args);    }    @Bean    public StringRedisTemplate redisTemplate() {        StringRedisTemplate template = new StringRedisTemplate(redisConnectionFactory());        // explicitly enable transaction support        template.setEnableTransactionSupport(true);        return template;    }    @Bean    public LettuceConnectionFactory redisConnectionFactory() {        return new LettuceConnectionFactory(new RedisStandaloneConfiguration("localhost", 6379));    }    @Bean    public PlatformTransactionManager transactionManager() throws SQLException, IOException {        return new DataSourceTransactionManager(dataSource);    }}

and this is my service method:

@Service@RequiredArgsConstructor@Slf4jpublic class TestService {   private final StringRedisTemplate redisTemplate;   private final UserRepository userRepository;   @Transactional               public void test() {       User test = User.builder()               .id(1001)               .name("test")               .email("test@mail.com")               .build();       userRepository.save(test);       Optional<User> userOpt = userRepository.findById(1001);       if(userOpt.isEmpty()){           throw new RuntimeException("not-found");       }       User user = userOpt.get();       user.setName("Test_2");       user.setEmail("Test_2@mail.com");       userRepository.save(user);       ValueOperations<String, String> values = redisTemplate.opsForValue();       values.set("my-key", user.get().getEmail());   }

However after the test method of TestService is called there is no user in MySQL db and I think it's because there is no active transaction for it.Is there any solution for this problem? Should I use spring ChainedTransactionManager class and then how? or I can only manage Redis transactions manually through MULTI?