chore(ecr): expose registryUri (#32176)

### Issue # (if applicable)

Closes #31631 

### Reason for this change


The Docker credentials helper (e.g. [docker-credential-ecr-login](https://github.com/awslabs/amazon-ecr-credential-helper)) expects a hostname in the configuration.

```json
{
	"credHelpers": {
		"public.ecr.aws": "ecr-login",
		"<aws_account_id>.dkr.ecr.<region>.amazonaws.com": "ecr-login"
	}
}
```
Docs: https://github.com/awslabs/amazon-ecr-credential-helper?tab=readme-ov-file#docker

### Description of changes


- Expose registryUri

### Description of how you validated changes


- 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-ecr/lib/repository.ts

@@ -49,6 +49,15 @@ export interface IRepository extends IResource {
    */
   readonly repositoryUri: string;
 
+  /**
+   * The URI of this repository's registry:
+   *
+   *    ACCOUNT.dkr.ecr.REGION.amazonaws.com
+   *
+   * @attribute
+   */
+  readonly registryUri: string;
+
   /**
    * Returns the URI of the repository for a certain tag. Can be used in `docker push/pull`.
    *
@@ -191,6 +200,17 @@ export abstract class RepositoryBase extends Resource implements IRepository {
     return this.repositoryUriForTag();
   }
 
+  /**
+   * The URI of this repository's registry:
+   *
+   *    ACCOUNT.dkr.ecr.REGION.amazonaws.com
+   *
+   */
+  public get registryUri(): string {
+    const parts = this.stack.splitArn(this.repositoryArn, ArnFormat.SLASH_RESOURCE_NAME);
+    return `${parts.account}.dkr.ecr.${parts.region}.${this.stack.urlSuffix}`;
+  }
+
   /**
    * Returns the URL of the repository. Can be used in `docker push/pull`.
    *

packages/aws-cdk-lib/aws-ecr/test/repository.test.ts

@@ -308,6 +308,30 @@ describe('repository', () => {
     });
   });
 
+  test('calculate registry URI', () => {
+    // GIVEN
+    const stack = new cdk.Stack();
+    const repo = new ecr.Repository(stack, 'Repo');
+
+    new cdk.CfnOutput(stack, 'RegistryUri', {
+      value: repo.registryUri,
+    });
+
+    // THEN
+    const arnSplit = { 'Fn::Split': [':', { 'Fn::GetAtt': ['Repo02AC86CF', 'Arn'] }] };
+    Template.fromStack(stack).hasOutput('*', {
+      'Value': {
+        'Fn::Join': ['', [
+          { 'Fn::Select': [4, arnSplit] },
+          '.dkr.ecr.',
+          { 'Fn::Select': [3, arnSplit] },
+          '.',
+          { Ref: 'AWS::URLSuffix' },
+        ]],
+      },
+    });
+  });
+
   test('import with concrete arn', () => {
     // GIVEN
     const stack = new cdk.Stack();