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/interfaces.go

@@ -0,0 +1,34 @@
+package database
+
+import (
+	"context"
+	"database/sql"
+)
+
+// DBTX matches the interface expected by SQLC-generated code
+// This interface is implemented by both *sql.DB and *sql.Tx
+type DBTX interface {
+	ExecContext(context.Context, string, ...interface{}) (sql.Result, error)
+	PrepareContext(context.Context, string) (*sql.Stmt, error)
+	QueryContext(context.Context, string, ...interface{}) (*sql.Rows, error)
+	QueryRowContext(context.Context, string, ...interface{}) *sql.Row
+}
+
+// BaseQuerier provides basic query functionality
+// This interface should be implemented by package-specific Queries types
+type BaseQuerier interface {
+	WithTx(tx *sql.Tx) BaseQuerier
+}
+
+// BaseQuerierTx provides transaction functionality
+// This interface should be implemented by package-specific Queries types
+type BaseQuerierTx interface {
+	BaseQuerier
+	Begin(ctx context.Context) (BaseQuerierTx, error)
+	Commit(ctx context.Context) error
+	Rollback(ctx context.Context) error
+}
+
+// TransactionFunc represents a function that operates within a database transaction
+// This is used by the shared transaction helpers in transaction.go
+type TransactionFunc[Q any] func(ctx context.Context, q Q) error