fix(backend/infrastructure/persistence/postgres): add testing connection to db and improve error messages

backend/internal/infrastructure/persistence/postgres/db.go

@@ -15,7 +15,7 @@ import (
 func New(dbURL string) (*pgxpool.Pool, error) {
 	poolConfig, err := pgxpool.ParseConfig(dbURL)
 	if err != nil {
-		return nil, fmt.Errorf("error while parsing connection string: %w", err)
+		return nil, fmt.Errorf("failed to parse connection string: %w", err)
 	}
 
 	poolConfig.MaxConns = 100
@@ -23,9 +23,13 @@ func New(dbURL string) (*pgxpool.Pool, error) {
 	poolConfig.MaxConnLifetime = time.Hour
 	poolConfig.HealthCheckPeriod = 30 * time.Second
 
-	db, err := pgxpool.NewWithConfig(context.Background(), poolConfig)
+	ctx := context.Background()
+	db, err := pgxpool.NewWithConfig(ctx, poolConfig)
 	if err != nil {
-		return nil, fmt.Errorf("error while initializing DB connections pool: %w", err)
+		return nil, fmt.Errorf("failed to initialize DB connections pool: %w", err)
+	}
+	if err = db.Ping(ctx); err != nil {
+		return nil, fmt.Errorf("failed to ping database: %w", err)
 	}
 	return db, nil
 }