CfnInclude: Cannot add metadata to NestedStack when including template

Describe the bug

When I try to add metadata to a stack that is created with CfnInclude I get the following error:

    at mergeObjectsWithoutDuplicates (/.../cfninclude-example/node_modules/aws-cdk-lib/core/lib/stack.js:2:854)

This seems confusing as I was trying to add a different metadata key/value pair via cdk.

Expected Behavior

I expected the templates to synthesize and the nested stack to have all metadata values

Current Behavior

No template is synthesized

Reproduction Steps

The template:

AWSTemplateFormatVersion: 2010-09-09
Metadata:
  some-data: "some-value"

Resources:
  MyBucket:
    Type: AWS::S3::Bucket
    Properties:
      BucketName: new-bucket

The CDK app:

#!/usr/bin/env node
import 'source-map-support/register';
import * as cdk from 'aws-cdk-lib';
import { Construct } from 'constructs';
import path = require('path');
import { CfnInclude } from 'aws-cdk-lib/cloudformation-include';

const app = new cdk.App();

class ParentStack extends cdk.Stack {
  constructor(scope: Construct, id: string, props?: cdk.StackProps) {
    super(scope, id, props);

    new CfnincludeExampleStack(this, 'CfnincludeExampleStack');
  }
}

class CfnincludeExampleStack extends cdk.NestedStack {
  constructor(scope: Construct, id: string, props?: cdk.StackProps) {
    super(scope, id, props);

    const template = new CfnInclude(this, 'CfnincludeTemplate', {
      templateFile: path.join('./include-stack.yaml'),
    });

    this.addMetadata('more-data', 'more-value');

    //This seems to work, but it's not the right way to do it
    //(Stack.of(template.stack).node.defaultChild as CfnStack).stack.addMetadata('more-data', 'more-value');
  }
}

new ParentStack(app, 'ParentStack');

Possible Solution

//This seems to work, but it's not the right way to do it
(Stack.of(template.stack).node.defaultChild as CfnStack).stack.addMetadata('more-data', 'more-value');

Additional Information/Context

This only happens with nested stacks.

CDK CLI Version

2.131.0 (build 92b912d)

Framework Version

No response

Node.js Version

v20.10.0

OS

MacOs Sonoma

Language

TypeScript

Language Version

5.3.3

Other information