feat: add PostgreSQL persistence layer with Neon DB support

internal/db/db.go

@@ -0,0 +1,29 @@
+package db
+
+import (
+	"context"
+	"fmt"
+	"time"
+
+	"github.com/jackc/pgx/v5/pgxpool"
+)
+
+func Open(databaseURL string) (*pgxpool.Pool, error) {
+	if databaseURL == "" {
+		return nil, fmt.Errorf("database URL is required")
+	}
+
+	ctx, cancel := context.WithTimeout(context.Background(), 10*time.Second)
+	defer cancel()
+
+	pool, err := pgxpool.New(ctx, databaseURL)
+	if err != nil {
+		return nil, fmt.Errorf("create connection pool: %w", err)
+	}
+
+	if err := pool.Ping(ctx); err != nil {
+		return nil, fmt.Errorf("ping database: %w", err)
+	}
+
+	return pool, nil
+}