Upgrading an RDS database with a custom parameter group

[Drumar]

I have created a database cluster with CDK, created a PostgreSQL 15.4 cluster. I created a custom parametergroup like this (java)

IParameterGroup  pmGroup = new ParameterGroup(this, "rds-cluster-parameters-" + majorVersion, ParameterGroupProps.builder()
                    .description("Database Parameter Group for PostgreSQL " + majorVersion)
                    .engine(engine)
                    .parameters(Map.of("search_path", "\"$user\",public"))
                    .build());

DatabaseClusterProps databaseClusterProps = DatabaseClusterProps.builder()
                .engine(engine)
                .clusterIdentifier(name)
                .vpc(networkResources.getVpc())
                .vpcSubnets(subnetSelection)
                .securityGroups(sgGroups)
                .serverlessV2MaxCapacity(CONFIG.getAws().getStack().getRdsCluster().getScaling().maxUnits)
                .serverlessV2MinCapacity(CONFIG.getAws().getStack().getRdsCluster().getScaling().minUnits)
                .credentials(dbMasterSecret)
                .parameterGroup(pmGroup)
                .storageType(DBClusterStorageType.AURORA_IOPT1)
                .storageEncryptionKey(storageEncryptionKey)
                .deletionProtection(deleteProtection)
                .removalPolicy(removalPolicy)
                .defaultDatabaseName(CONFIG.getAws().getStack().getRdsCluster().getDefaultDatabaseName())
                .storageEncrypted(true)
                .iamAuthentication(false)
                .writer(ClusterInstance.serverlessV2("writer", ServerlessV2ClusterInstanceProps.builder()
                                .parameterGroup(pmGroup)
                                .autoMinorVersionUpgrade(true)
                                .allowMajorVersionUpgrade(false)
                                .build()))
               .readers(List.of()).build();
DatabaseCluster myCluster=new DatabaseCluster(this,"RDS Cluster", databaseClusterProps);

When I change the config to use version 16.1 instead deploying the stack throws an error:

Deployment failed: Error: The stack named AuroraRegionalServerlessClusterStack failed to deploy: UPDATE_ROLLBACK_COMPLETE: Resource handler returned message: "The current DB instance parameter group auroraregionalserverlessclusterstack-rdsclusterparameters15instanceparametergroup9b8f89a2-ohjwbiih2vzd is custom. You must explicitly specify a new DB instance parameter group, either default or custom, for the engine version upgrade. (Service: Rds, Status Code: 400, Request ID: 40c0e300-d69f-4b24-ab30-ce69da729cc3)" (RequestToken: 039ba251-9331-77e5-1086-3169ee9d5b12, HandlerErrorCode: InvalidRequest)

The question is: how can I realize a major version upgrade by updating the stack (configuration)? I tried to add a configuration item with a boolean to indicate a major version upgrade, and in that case create a new parameter group, but that does not seem to help me very much.