fix: Address review comments — restore metric name and add Prometheus scrape test

- Restore gauge name to 'db.connections.total' so Micrometer's Prometheus
  naming convention exposes it as 'db_connections_total', preserving
  backward compatibility with existing dashboards.
- Add prometheusScrapExposesDbConnectionsTotal() test that uses
  PrometheusMeterRegistry to verify the Prometheus scrape output contains
  'db_connections_total' as a gauge type.

Author: RajdeepKushwaha5

openmetadata-service/src/main/java/org/openmetadata/service/monitoring/OpenMetadataMetrics.java

@@ -50,7 +50,7 @@ public OpenMetadataMetrics(MeterRegistry meterRegistry) {
             .sla(LATENCY_SLA_BUCKETS)
             .register(meterRegistry);
 
-    Gauge.builder("db.connections", () -> poolTotalConnections())
+    Gauge.builder("db.connections.total", () -> poolTotalConnections())
         .description("Total connections in the database connection pool")
         .register(meterRegistry);
 

openmetadata-service/src/test/java/org/openmetadata/service/monitoring/OpenMetadataMetricsTest.java

@@ -2,9 +2,12 @@
 
 import static org.junit.jupiter.api.Assertions.assertEquals;
 import static org.junit.jupiter.api.Assertions.assertNotNull;
+import static org.junit.jupiter.api.Assertions.assertTrue;
 
 import io.micrometer.core.instrument.Gauge;
 import io.micrometer.core.instrument.simple.SimpleMeterRegistry;
+import io.micrometer.prometheusmetrics.PrometheusConfig;
+import io.micrometer.prometheusmetrics.PrometheusMeterRegistry;
 import java.util.concurrent.atomic.AtomicInteger;
 import org.junit.jupiter.api.BeforeEach;
 import org.junit.jupiter.api.Test;
@@ -30,8 +33,8 @@ void dbConnectionsTotalReflectsHikariCPPoolSize() {
 
     new OpenMetadataMetrics(registry);
 
-    Gauge total = registry.find("db.connections").gauge();
-    assertNotNull(total, "db.connections gauge should be registered");
+    Gauge total = registry.find("db.connections.total").gauge();
+    assertNotNull(total, "db.connections.total gauge should be registered");
     assertEquals(20.0, total.value(), 0.01, "Should equal active + idle");
 
     activeConnections.set(10);
@@ -47,8 +50,31 @@ void dbConnectionsTotalReflectsHikariCPPoolSize() {
   void dbConnectionsTotalReturnsZeroWithoutHikariCP() {
     new OpenMetadataMetrics(registry);
 
-    Gauge total = registry.find("db.connections").gauge();
-    assertNotNull(total, "db.connections gauge should be registered");
+    Gauge total = registry.find("db.connections.total").gauge();
+    assertNotNull(total, "db.connections.total gauge should be registered");
     assertEquals(0.0, total.value(), 0.01, "Should be zero when HikariCP metrics are absent");
   }
+
+  @Test
+  void prometheusScrapExposesDbConnectionsTotal() {
+    PrometheusMeterRegistry promRegistry = new PrometheusMeterRegistry(PrometheusConfig.DEFAULT);
+
+    AtomicInteger activeConnections = new AtomicInteger(3);
+    AtomicInteger idleConnections = new AtomicInteger(7);
+
+    Gauge.builder("hikaricp.connections.active", activeConnections, AtomicInteger::doubleValue)
+        .register(promRegistry);
+    Gauge.builder("hikaricp.connections.idle", idleConnections, AtomicInteger::doubleValue)
+        .register(promRegistry);
+
+    new OpenMetadataMetrics(promRegistry);
+
+    String scrape = promRegistry.scrape();
+    assertTrue(
+        scrape.contains("db_connections_total"),
+        "Prometheus scrape should contain db_connections_total metric");
+    assertTrue(
+        scrape.contains("# TYPE db_connections_total gauge"),
+        "db_connections_total should be exposed as a gauge type");
+  }
 }