chore(rds): add clusterArn property to DatabaseCluster (#29133)

### Issue # (if applicable)

### Reason for this change

This is to bring parity with #10741, we need the cluster arn to enable data api manually waiting for #28574.

### Description of changes

This adds a clusterArn property to IDatabaseCluster

### Description of how you validated changes

The changes have been validated through a unit test

### Checklist
- [x] My code adheres to the [CONTRIBUTING GUIDE](https://github.com/aws/aws-cdk/blob/main/CONTRIBUTING.md) and [DESIGN GUIDELINES](https://github.com/aws/aws-cdk/blob/main/docs/DESIGN_GUIDELINES.md)

----

*By submitting this pull request, I confirm that my contribution is made under the terms of the Apache-2.0 license*

packages/aws-cdk-lib/aws-rds/lib/cluster-ref.ts

@@ -50,6 +50,11 @@ export interface IDatabaseCluster extends IResource, ec2.IConnectable, secretsma
    */
   readonly engine?: IClusterEngine;
 
+  /**
+   * The ARN of the database cluster
+   */
+  readonly clusterArn: string;
+
   /**
    * Add a new db proxy to this cluster.
    */

packages/aws-cdk-lib/aws-rds/lib/cluster.ts

@@ -457,6 +457,18 @@ export abstract class DatabaseClusterBase extends Resource implements IDatabaseC
    */
   public abstract readonly connections: ec2.Connections;
 
+  /**
+   * The ARN of the cluster
+   */
+  public get clusterArn(): string {
+    return Stack.of(this).formatArn({
+      service: 'rds',
+      resource: 'cluster',
+      arnFormat: ArnFormat.COLON_RESOURCE_NAME,
+      resourceName: this.clusterIdentifier,
+    });
+  }
+
   /**
    * Add a new db proxy to this cluster.
    */

packages/aws-cdk-lib/aws-rds/test/cluster.test.ts

@@ -4052,6 +4052,38 @@ describe('cluster', () => {
       ],
     });
   });
+
+  test('clusterArn property', () => {
+    // GIVEN
+    const stack = testStack();
+    const vpc = ec2.Vpc.fromLookup(stack, 'VPC', { isDefault: true });
+    const cluster = new DatabaseCluster(stack, 'Database', {
+      engine: DatabaseClusterEngine.auroraPostgres({ version: AuroraPostgresEngineVersion.VER_14_3 }),
+      instanceProps: { vpc },
+    });
+    const exportName = 'DbCluterArn';
+
+    // WHEN
+    new cdk.CfnOutput(stack, exportName, {
+      exportName,
+      value: cluster.clusterArn,
+    });
+
+    // THEN
+    expect(
+      stack.resolve(cluster.clusterArn),
+    ).toEqual({
+      'Fn::Join': [
+        '',
+        [
+          'arn:',
+          { Ref: 'AWS::Partition' },
+          ':rds:us-test-1:12345:cluster:',
+          { Ref: 'DatabaseB269D8BB' },
+        ],
+      ],
+    });
+  });
 });
 
 test.each([