chore(amplify): domain name validation (#31959)

### Issue # (if applicable)

None

### Reason for this change

We can configure amplify domain name but there is no validation for that.

### Description of changes

Add validation for an amplify domain name
- length must be lower than 255 characters
- match with [the regular expression](https://docs.aws.amazon.com/AWSCloudFormation/latest/UserGuide/aws-resource-amplify-domain.html#cfn-amplify-domain-domainname)
  - /^(((?!-)[A-Za-z0-9-]{0,62}[A-Za-z0-9])\.)+((?!-)[A-Za-z0-9-]{1,62}[A-Za-z0-9])(\.)?$/

### Description of how you validated changes

Add 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/aws-amplify-alpha/lib/domain.ts

@@ -1,6 +1,6 @@
 import * as acm from 'aws-cdk-lib/aws-certificatemanager';
 import * as iam from 'aws-cdk-lib/aws-iam';
-import { Lazy, Resource, IResolvable } from 'aws-cdk-lib/core';
+import { Lazy, Resource, IResolvable, Token } from 'aws-cdk-lib/core';
 import { Construct } from 'constructs';
 import { CfnDomain } from 'aws-cdk-lib/aws-amplify';
 import { IApp } from './app';
@@ -131,6 +131,13 @@ export class Domain extends Resource {
     this.subDomains = props.subDomains || [];
 
     const domainName = props.domainName || id;
+    if (!Token.isUnresolved(domainName) && domainName.length > 255) {
+      throw new Error(`Domain name must be 255 characters or less, got: ${domainName.length} characters.`);
+    }
+    if (!Token.isUnresolved(domainName) && !/^(((?!-)[A-Za-z0-9-]{0,62}[A-Za-z0-9])\.)+((?!-)[A-Za-z0-9-]{1,62}[A-Za-z0-9])(\.)?$/.test(domainName)) {
+      throw new Error(`Domain name must be a valid hostname, got: ${domainName}.`);
+    }
+
     const domain = new CfnDomain(this, 'Resource', {
       appId: props.app.appId,
       domainName,

packages/@aws-cdk/aws-amplify-alpha/test/domain.test.ts

@@ -176,6 +176,55 @@ test('map a branch to the domain root', () => {
   });
 });
 
+test('throw error for invalid domain name length', () => {
+  const stack = new Stack();
+  const app = new amplify.App(stack, 'App', {
+    sourceCodeProvider: new amplify.GitHubSourceCodeProvider({
+      owner: 'aws',
+      repository: 'aws-cdk',
+      oauthToken: SecretValue.unsafePlainText('secret'),
+    }),
+  });
+  const prodBranch = app.addBranch('main');
+
+  expect(() => app.addDomain('Domain', {
+    subDomains: [
+      {
+        branch: prodBranch,
+        prefix: 'prod',
+      },
+    ],
+    domainName: 'a'.repeat(256),
+  })).toThrow('Domain name must be 255 characters or less, got: 256 characters.');
+});
+
+test.each([
+  '-example.com',
+  'example..com',
+  'example.com-',
+  '[email protected]',
+])('throw error for invalid domain name', (domainName) => {
+  const stack = new Stack();
+  const app = new amplify.App(stack, 'App', {
+    sourceCodeProvider: new amplify.GitHubSourceCodeProvider({
+      owner: 'aws',
+      repository: 'aws-cdk',
+      oauthToken: SecretValue.unsafePlainText('secret'),
+    }),
+  });
+  const prodBranch = app.addBranch('main');
+
+  expect(() => app.addDomain('Domain', {
+    subDomains: [
+      {
+        branch: prodBranch,
+        prefix: 'prod',
+      },
+    ],
+    domainName,
+  })).toThrow(`Domain name must be a valid hostname, got: ${domainName}.`);
+});
+
 test('throws at synthesis without subdomains', () => {
   // GIVEN
   const app = new App();

packages/@aws-cdk/aws-amplify-alpha/test/integ.app-custom-domain.js.snapshot/cdk-amplify-app-custom-domain.template.json

@@ -99,7 +99,7 @@
     "EnablePullRequestPreview": true
    }
   },
-  "Appexamplecom6AF1A3AD": {
+  "Appexamplecom93D8EC68": {
    "Type": "AWS::Amplify::Domain",
    "Properties": {
     "AppId": {
@@ -124,7 +124,7 @@
       "Ref": "Certificate4E7ABB08"
      }
     },
-    "DomainName": "*.example.com",
+    "DomainName": "example.com",
     "EnableAutoSubDomain": false,
     "SubDomainSettings": [
      {
@@ -156,10 +156,10 @@
   "Certificate4E7ABB08": {
    "Type": "AWS::CertificateManager::Certificate",
    "Properties": {
-    "DomainName": "*.*.example.com",
+    "DomainName": "*.example.com",
     "DomainValidationOptions": [
      {
-      "DomainName": "*.*.example.com",
+      "DomainName": "*.example.com",
       "HostedZoneId": "Z23ABC4XYZL05B"
      }
     ],