Why can't I obtain the metric data in Flink?

### Bug Description

**What happened:**
When I was using Flink to write data to Hudi, I wanted to obtain the metric information during the writing process.
The only information I obtained in the Metric class is key = "sink_table.index.type", value = 6.Why can't we obtain the metric information?
flink1.20.3
hudi 1.1.1
**What you expected:**
I will eventually write the metric information to MySQL.
**Steps to reproduce:**
public class MetricNew extends AbstractUserDefinedMetricsReporter {

private static final Logger log = LogManager.getLogger(MetricNew.class);

private final ScheduledExecutorService exec =
Executors.newSingleThreadScheduledExecutor(r -> {
Thread t = new Thread(r, "hudi-user-metrics-reporter");
t.setDaemon(true);
return t;
});

public MetricNew(Properties props, MetricRegistry registry) {
super(props, registry);
}

/**
* ⚠️ Flink 场景下必须自己调度 report
*/
@Override
public void start() {
// 延迟 10s 后开始，每 30s 打印一次
exec.scheduleAtFixedRate(this::report, 10, 30, TimeUnit.SECONDS);
log.info("MetricNew started, schedule metrics report");
}

/**
* 只做一件事：打印 registry 里已有的 metrics
*/
@Override
public void report() {
try {
if (getRegistry() == null || getRegistry().getGauges().isEmpty()) {
log.info("No gauges found in MetricRegistry");
return;
}

getRegistry().getGauges().forEach((key, value) -> {
Object v;
try {
v = value.getValue();
} catch (Exception e) {
v = "N/A";
}
log.info("[HUDI-METRIC] key=" + key + ", value=" + v);
});
} catch (Throwable t) {
log.error("MetricNew report failed", t);
}
}

@Override
public void stop() {
exec.shutdownNow();
log.info("MetricNew stopped");
}
}

### Environment

**Hudi version:**
**Query engine:** (Spark/Flink/Trino etc)
**Relevant configs:**

### Logs and Stack Trace

_No response_

Start with the AbstractUserDefinedMetricsReporter implementation and the MetricRegistry usage shown in MetricNew, then reproduce the report with Flink 1.20.3 and Hudi 1.1.1. Check why the registry exposes only sink_table.index.type and determine what configuration or integration is needed for the expected metrics to be available for writing to MySQL.

Written by the indexing model from the issue text.