DatabaseCluster.clusterEndpoint.hostname does not respect LOCALSTACK_HOSTNAME

When deploying my RDS stack I have it put it's hostname into an SSM Parameter to be used by Lambda functions later. This doesn't seem to work when configuring LOCALSTACK_HOSTNAME, HOSTNAME and HOSTNAME_EXTERNAL.

Given the following docker-compose.yaml and cdk files

version: "3.5"
services:
  localstack:
    container_name: "localstack"
    image: localstack/localstack:latest
    network_mode: bridge
    ports:
      - "80:80"
      - "443:443"
      - "4566:4566"
      - "4510-4559:4510-4559"  # external services port range
      - "127.0.0.1:53:53"                # DNS config (only required for Pro)
      - "127.0.0.1:53:53/udp"            # DNS config (only required for Pro)
      - "4571:4571"
    environment:
      - SERVICES=sqs, lambda, apigateway, s3, sts, ssm, cloudformation, ecr, kms, iam, rds
      - LOCALSTACK_HOSTNAME=172.26.0.1
      - HOSTNAME=172.26.0.1
      - HOSTNAME_EXTERNAL=172.26.0.1
      - DOCKER_HOST=unix:///var/run/docker.sock
      - DEFAULT_REGION=eu-west-2
      - TEST_AWS_ACCOUNT_ID=000000000000
    volumes:
      - "${TMPDIR:-/tmp/localstack}:/tmp/localstack"
      - "/var/run/docker.sock:/var/run/docker.sock"

import { App, Stack } from "aws-cdk-lib";
import { Construct } from "constructs";
import { StringParameter } from "aws-cdk-lib/aws-ssm";
import {
  AuroraPostgresEngineVersion,
  DatabaseCluster,
  DatabaseClusterEngine,
} from "aws-cdk-lib/aws-rds";
import { Vpc } from "aws-cdk-lib/aws-ec2";

class TestStack extends Stack {
  constructor(scope: Construct, id: string) {
    super(scope, id);

    new DbConstruct(this, "consumer");
  }
}

class DbConstruct extends Construct {
  constructor(scope: Construct, id: string) {
    super(scope, id);

    const cluster = new DatabaseCluster(this, "DatabaseCluster", {
      engine: DatabaseClusterEngine.auroraPostgres({
        version: AuroraPostgresEngineVersion.VER_13_4,
      }),
      defaultDatabaseName: "database",
      storageEncrypted: true,
      instanceProps: {
        vpc: new Vpc(this, "db-vpc"),
      },
    });

    new StringParameter(this, `DatabaseEndpoint`, {
      parameterName: "databaseEndpoint",
      stringValue: cluster.clusterEndpoint.hostname,
    });
  }
}

const app = new App();

new TestStack(app, "stack");

I get the following results when querying by console

$ awslocal ssm get-parameter --name databaseEndpoint
{
    "Parameter": {
        "Name": "databaseEndpoint",
        "Type": "String",
        "Value": "localhost",
        "Version": 1,
        "LastModifiedDate": "2022-08-03T15:36:53.410000+01:00",
        "ARN": "arn:aws:ssm:eu-west-2:000000000000:parameter/databaseEndpoint",
        "DataType": "text"
    }
}

$ awslocal rds describe-db-clusters
{
    "DBClusters": [
        {
            "AllocatedStorage": 1,
            "DatabaseName": "database",
            "DBClusterIdentifier": "dbc-63393c9f",
            "DBClusterParameterGroup": "default.aurora-postgresql13",
            "DBSubnetGroup": "consumerDatabaseClusterSubnets68C9D7B3-baf5d77a",
            "Status": "error",
            "Endpoint": "172.26.0.1:4511",
            "MultiAZ": false,
            "Engine": "aurora-postgresql",
            "EngineVersion": "13.4",
            "Port": 4511,
            "MasterUsername": "postgres",
            "StorageEncrypted": false,
            "DBClusterArn": "arn:aws:rds:eu-west-2:000000000000:cluster:dbc-63393c9f",
            "IAMDatabaseAuthenticationEnabled": false,
            "CopyTagsToSnapshot": true
        }
    ]
}

Of note here is that the endpoint from describe-db-clusters is 172.26.0.1:4511 whereas the value that gets stored in ssm is localhost

localstack / aws-cdk-local

DatabaseCluster.clusterEndpoint.hostname does not respect LOCALSTACK_HOSTNAME #73