database: create shared database package with configurable patterns

Extract ~200 lines of duplicate database connection code from api/ntpdb/
and monitor/ntpdb/ into common/database/ package. Creates foundation for
database consolidation while maintaining zero breaking changes.

Files added:
- config.go: Unified configuration with package-specific defaults
- connector.go: Dynamic connector pattern from Boostport
- pool.go: Configurable connection pool management
- metrics.go: Optional Prometheus metrics integration
- interfaces.go: Shared database interfaces for consistent patterns

Key features:
- Configuration-driven approach (API: 25/10 connections + metrics,
  Monitor: 10/5 connections, no metrics)
- Optional Prometheus metrics when registerer provided
- Backward compatibility via convenience functions
- Flexible config file loading (explicit paths + search-based)

Dependencies: Added mysql driver and yaml parsing for database configuration.

database/metrics.go

@@ -0,0 +1,93 @@
+package database
+
+import (
+	"context"
+	"database/sql"
+	"fmt"
+	"time"
+
+	"github.com/prometheus/client_golang/prometheus"
+)
+
+// DatabaseMetrics holds the Prometheus metrics for database connection pool monitoring
+type DatabaseMetrics struct {
+	ConnectionsOpen         prometheus.Gauge
+	ConnectionsIdle         prometheus.Gauge
+	ConnectionsInUse        prometheus.Gauge
+	ConnectionsWaitCount    prometheus.Counter
+	ConnectionsWaitDuration prometheus.Histogram
+}
+
+// NewDatabaseMetrics creates a new set of database metrics and registers them
+func NewDatabaseMetrics(registerer prometheus.Registerer) *DatabaseMetrics {
+	metrics := &DatabaseMetrics{
+		ConnectionsOpen: prometheus.NewGauge(prometheus.GaugeOpts{
+			Name: "database_connections_open",
+			Help: "Number of open database connections",
+		}),
+		ConnectionsIdle: prometheus.NewGauge(prometheus.GaugeOpts{
+			Name: "database_connections_idle",
+			Help: "Number of idle database connections",
+		}),
+		ConnectionsInUse: prometheus.NewGauge(prometheus.GaugeOpts{
+			Name: "database_connections_in_use",
+			Help: "Number of database connections in use",
+		}),
+		ConnectionsWaitCount: prometheus.NewCounter(prometheus.CounterOpts{
+			Name: "database_connections_wait_count_total",
+			Help: "Total number of times a connection had to wait",
+		}),
+		ConnectionsWaitDuration: prometheus.NewHistogram(prometheus.HistogramOpts{
+			Name:    "database_connections_wait_duration_seconds",
+			Help:    "Time spent waiting for a database connection",
+			Buckets: prometheus.DefBuckets,
+		}),
+	}
+
+	if registerer != nil {
+		registerer.MustRegister(
+			metrics.ConnectionsOpen,
+			metrics.ConnectionsIdle,
+			metrics.ConnectionsInUse,
+			metrics.ConnectionsWaitCount,
+			metrics.ConnectionsWaitDuration,
+		)
+	}
+
+	return metrics
+}
+
+// monitorConnectionPool runs a background goroutine to collect connection pool metrics
+func monitorConnectionPool(ctx context.Context, db *sql.DB, registerer prometheus.Registerer) {
+	if registerer == nil {
+		return // No metrics collection if no registerer provided
+	}
+
+	metrics := NewDatabaseMetrics(registerer)
+	ticker := time.NewTicker(30 * time.Second)
+	defer ticker.Stop()
+
+	for {
+		select {
+		case <-ctx.Done():
+			return
+		case <-ticker.C:
+			stats := db.Stats()
+
+			metrics.ConnectionsOpen.Set(float64(stats.OpenConnections))
+			metrics.ConnectionsIdle.Set(float64(stats.Idle))
+			metrics.ConnectionsInUse.Set(float64(stats.InUse))
+			metrics.ConnectionsWaitCount.Add(float64(stats.WaitCount))
+
+			if stats.WaitDuration > 0 {
+				metrics.ConnectionsWaitDuration.Observe(stats.WaitDuration.Seconds())
+			}
+
+			// Log connection pool stats for high usage or waiting
+			if stats.OpenConnections > 20 || stats.WaitCount > 0 {
+				fmt.Printf("Connection pool stats: open=%d idle=%d in_use=%d wait_count=%d wait_duration=%s\n",
+					stats.OpenConnections, stats.Idle, stats.InUse, stats.WaitCount, stats.WaitDuration)
+			}
+		}
+	}
+}