[metrics] Add partition count metrics for tables and cluster monitoring (#1662)

* [FLUSS-1571] Add partition count metric for cluster monitoring

- Add PARTITION_COUNT metric name constant
- Implement getTotalPartitionCount() in CoordinatorContext
- Add partition count metric registration and updates in CoordinatorEventManager
- Follow existing TABLE_COUNT metric implementation pattern
- Add basic tests for partition count functionality

This provides a simple way to monitor total partition count across the cluster,
helping users identify when too many partitions might cause cluster instability.

* [FLUSS-1571] [docs] Add partition count metrics documentation

- Add partitionCount metric documentation for cluster-level monitoring
- Document the new metric that tracks total number of partitions in the cluster
- This metric helps users monitor partition distribution and identify potential cluster instability issues

* [FLUSS-1571] [docs] Fix table rowspan for partition count metrics

Author: buvb

fluss-common/src/main/java/org/apache/fluss/metrics/MetricNames.java

@@ -40,6 +40,7 @@ public class MetricNames {
     public static final String OFFLINE_BUCKET_COUNT = "offlineBucketCount";
     public static final String TABLE_COUNT = "tableCount";
     public static final String BUCKET_COUNT = "bucketCount";
+    public static final String PARTITION_COUNT = "partitionCount";
     public static final String REPLICAS_TO_DELETE_COUNT = "replicasToDeleteCount";
 
     // for coordinator event processor

fluss-server/src/main/java/org/apache/fluss/server/coordinator/CoordinatorContext.java

@@ -657,4 +657,8 @@ public void resetContext() {
         liveTabletServers.clear();
         shuttingDownTabletServers.clear();
     }
+
+    public int getTotalPartitionCount() {
+        return partitionAssignments.size();
+    }
 }

fluss-server/src/main/java/org/apache/fluss/server/coordinator/event/CoordinatorEventManager.java

@@ -66,6 +66,7 @@ public final class CoordinatorEventManager implements EventManager {
     private volatile int offlineBucketCount;
     private volatile int tableCount;
     private volatile int bucketCount;
+    private volatile int partitionCount;
     private volatile int replicasToDeleteCount;
 
     private static final int WINDOW_SIZE = 100;
@@ -91,6 +92,7 @@ private void registerMetrics() {
         coordinatorMetricGroup.gauge(MetricNames.OFFLINE_BUCKET_COUNT, () -> offlineBucketCount);
         coordinatorMetricGroup.gauge(MetricNames.BUCKET_COUNT, () -> bucketCount);
         coordinatorMetricGroup.gauge(MetricNames.TABLE_COUNT, () -> tableCount);
+        coordinatorMetricGroup.gauge(MetricNames.PARTITION_COUNT, () -> partitionCount);
         coordinatorMetricGroup.gauge(
                 MetricNames.REPLICAS_TO_DELETE_COUNT, () -> replicasToDeleteCount);
     }
@@ -104,6 +106,7 @@ private void updateMetricsViaAccessContext() {
                             int tabletServerCount = context.getLiveTabletServers().size();
                             int tableCount = context.allTables().size();
                             int bucketCount = context.bucketLeaderAndIsr().size();
+                            int partitionCount = context.getTotalPartitionCount();
                             int offlineBucketCount = context.getOfflineBucketCount();
 
                             int replicasToDeletes = 0;
@@ -135,6 +138,7 @@ private void updateMetricsViaAccessContext() {
                                     tabletServerCount,
                                     tableCount,
                                     bucketCount,
+                                    partitionCount,
                                     offlineBucketCount,
                                     replicasToDeletes);
                         });
@@ -147,6 +151,7 @@ private void updateMetricsViaAccessContext() {
             this.tabletServerCount = metricsData.tabletServerCount;
             this.tableCount = metricsData.tableCount;
             this.bucketCount = metricsData.bucketCount;
+            this.partitionCount = metricsData.partitionCount;
             this.offlineBucketCount = metricsData.offlineBucketCount;
             this.replicasToDeleteCount = metricsData.replicasToDeleteCount;
         } catch (Exception e) {
@@ -268,18 +273,21 @@ private static class MetricsData {
         private final int tabletServerCount;
         private final int tableCount;
         private final int bucketCount;
+        private final int partitionCount;
         private final int offlineBucketCount;
         private final int replicasToDeleteCount;
 
         public MetricsData(
                 int tabletServerCount,
                 int tableCount,
                 int bucketCount,
+                int partitionCount,
                 int offlineBucketCount,
                 int replicasToDeleteCount) {
             this.tabletServerCount = tabletServerCount;
             this.tableCount = tableCount;
             this.bucketCount = bucketCount;
+            this.partitionCount = partitionCount;
             this.offlineBucketCount = offlineBucketCount;
             this.replicasToDeleteCount = replicasToDeleteCount;
         }

website/docs/maintenance/observability/monitor-metrics.md

@@ -294,8 +294,8 @@ Some metrics might not be exposed when using other JVM implementations (e.g. IBM
   </thead>
   <tbody>
     <tr>
-      <th rowspan="12"><strong>coordinator</strong></th>
-      <td style={{textAlign: 'center', verticalAlign: 'middle' }} rowspan="7">-</td>
+      <th rowspan="13"><strong>coordinator</strong></th>
+      <td style={{textAlign: 'center', verticalAlign: 'middle' }} rowspan="8">-</td>
       <td>activeCoordinatorCount</td>
       <td>The number of active CoordinatorServer in this cluster.</td>
       <td>Gauge</td>
@@ -320,6 +320,11 @@ Some metrics might not be exposed when using other JVM implementations (e.g. IBM
       <td>The total number of buckets in this cluster.</td>
       <td>Gauge</td>
     </tr>
+    <tr>
+      <td>partitionCount</td>
+      <td>The total number of partitions in this cluster.</td>
+      <td>Gauge</td>
+    </tr>
     <tr>
       <td>replicasToDeleteCount</td>
       <td>The total number of replicas in the progress to be deleted in this cluster.</td>