This is the lowest-cost I like.

You can go for serverless_v2_min_capacity set to 0 (zero), for absolute minimum cost.

        ### Aurora Serverless v2 Cluster for PostgreSQL-v16
        self.db = aws_rds.DatabaseCluster( self,
            ### ??? NOT-Serverless
            ### https://docs.aws.amazon.com/cdk/api/v2/python/aws_cdk.aws_rds/DatabaseCluster.html
            id="AuroraV2-PGSQL",
            default_database_name = default_database_name,
            cluster_identifier = cluster_identifier,
            engine = aws_rds.DatabaseClusterEngine.aurora_postgres(version=aws_rds.AuroraPostgresEngineVersion.VER_16_4),
            enable_data_api = True, ### Default = False
            auto_minor_version_upgrade = False,
            writer=aws_rds.ClusterInstance.serverless_v2( id="AuroraWriter",
                instance_identifier = f"{cluster_identifier}-writer",
                #__ scale_with_writer =  .. .. applies to READERs only
                auto_minor_version_upgrade = False,
                allow_major_version_upgrade = False,
                publicly_accessible = False,
            ),
             #__ readers = [IClusterInstance] ### A list of instances to create as cluster-reader-instances. Default: - no readers are created. The cluster will have a single writer/reader
            serverless_v2_min_capacity = 1.0,  # DEFAULT is 0.5 (lowest possible)
            serverless_v2_max_capacity = serverless_aurorav2_max_capacity,
            # instances = [0-9]+, ### !!!!! LEGACY DEPRECATED parameter !!!  DEFAULT = 2 (Writer + 1-Reader)
            ### In V1-Aurora, we have to EXPLICITY provide the secret.  Not so for V2!
            ### In V2-Aurora, Default-CDK-construct's behavior is to create a NEW username of 'admin' (or 'postgres' for PostgreSQL) and SecretsManager-generated password
            # credentials=aws_rds.Credentials.from_secret(
            #     secret = self.rds_admin_dbo_secret,
            #     username = "admin_user"
            # ),
           # parameter_group=aws_rds.ParameterGroup.from_parameter_group_name(
            #     self,
            #     "ParameterGroup",
            #     f"default.aurora-postgresql{engine_ver_as_string}"
            # ),
            # network_type=aws_rds.NetworkType.IPV4,
            # enable_local_write_forwarding = True, ## Whether read-replicas can forward write-operations to the writer-nstance. Only be enabled for MySQL 3.04+ or PostgreSQL 16.4+

            backup=aws_rds.BackupProps(retention=Duration.days(30),
            copy_tags_to_snapshot = True,
            deletion_protection = True,
            removal_policy = RemovalPolicy.RETAIN_ON_UPDATE_OR_DELETE,
            vpc=vpc
            subnet_group=self.rds_subnet_group,
            security_groups=[self.rds_security_group],
            # storage_type = aws_rds.DBClusterStorageType.AURORA_IOPT1, ### required for LIMITLESS mode
            # storage_type = aws_rds.DBClusterStorageType.AURORA, ### Default: - DBClusterStorageType.AURORA_IOPT1
            # instance_props=aws_rds.InstanceProps( !!!!!!!!!!!!!!!!!!! LEGACY DEPRECATED parameter !!!!!!!!!!!!!!!!!!!!
            #     # parameter_group = aws_rds.ParameterGroup.from_parameter_group_name( self, "ParamGrp", rds_paramgroup_name),
            #     vpc=self.vpc, ### WARNING: RuntimeError: Provide either vpc or instanceProps.vpc, but not both
            #     vpc_subnets = vpc_subnets, ### WARNING: RuntimeError: Provide either vpc or instanceProps.vpc, but not both
            #     security_groups=[self.rds_security_group], ### WARNING: RuntimeError: Provide either vpc or instanceProps.vpc, but not both
            #     allow_major_version_upgrade = False,
            #     publicly_accessible = False,
            #     delete_automated_backups = False,
            #     instance_type=aws_ec2.InstanceType.of( !!!!!!! LEGACY DEPRECATED parameter !!!!!!!!
            #         aws_ec2.InstanceClass.R6GD,
            #         aws_ec2.InstanceSize.XLARGE4,
            #     ),
            # ),

            # cluster_scailability_type=aws_rds.ClusterScailabilityType.STANDARD,
            # enable_performance_insights=True, ### RuntimeError: Performance Insights must be enabled for Aurora Limitless Database.
            # performance_insight_retention=aws_rds.PerformanceInsightRetention.MONTHS_1,
            # enable_cluster_level_enhanced_monitoring=True,  ### RuntimeError: Cluster level enhanced monitoring must be set for Aurora Limitless Database. Please set 'monitoringInterval' and enable 'enableClusterLevelEnhancedMonitoring'.
            # monitoring_interval=Duration.seconds(60),       ### Max 1 minute. RuntimeError: Cluster level enhanced monitoring must be set for Aurora Limitless Database. Please set 'monitoringInterval' and enable 'enableClusterLevelEnhancedMonitoring'.
                                        ### Default: NO enhanced monitoring
            # monitoring_role -- Default: Role is Automatically created -- will be used to manage DB instances monitoring
            # cloudwatch_logs_exports = [str] ###  list of log-types that need to be enabled, for exporting to CW-Logs. Default: - --NO-- log exports
            # cloudwatch_logs_retention = RetentionDays() ### Default: - logs --NEVER-- expire.  # of days log-events are kept in CW-Logs. To remove the retention policy, set the value to Infinity.

            # backtrack_window = .. MySql only.
            # s3_export_buckets = .. MySql only.
            # s3_import_buckets = .. MySql only.
        )