fix(route53-targets): ApiGateway does not accept RestApiBase (#16610)

Closes #16227.

----

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

Author: kaizencc

Diff for: packages/@aws-cdk/aws-route53-targets/lib/api-gateway-domain-name.ts

@@ -26,7 +26,7 @@ export class ApiGatewayDomain implements route53.IAliasRecordTarget {
  * `ApiGatewayDomain` class.
  */
 export class ApiGateway extends ApiGatewayDomain {
-  constructor(api: apig.RestApi) {
+  constructor(api: apig.RestApiBase) {
     if (!api.domainName) {
       throw new Error('API does not define a default domain name');
     }

Diff for: packages/@aws-cdk/aws-route53-targets/test/apigateway-target.test.ts

@@ -106,3 +106,51 @@ test('fails if an ApiGateway is used with an API that does not define a domain n
     });
   }).toThrow(/API does not define a default domain name/);
 });
+
+test('targets.ApiGateway accepts a SpecRestApi', () => {
+  // GIVEN
+  const stack = new Stack();
+  const cert = new acm.Certificate(stack, 'cert', { domainName: 'example.com' });
+  const api = new apigw.SpecRestApi(stack, 'api', {
+    domainName: {
+      domainName: 'example.com',
+      certificate: cert,
+    },
+    apiDefinition: apigw.ApiDefinition.fromInline({
+      key1: 'val1',
+    }),
+  });
+  const zone = new route53.HostedZone(stack, 'zone', {
+    zoneName: 'example.com',
+  });
+  api.root.addMethod('GET');
+
+  // WHEN
+  new route53.ARecord(stack, 'A', {
+    zone,
+    target: route53.RecordTarget.fromAlias(new targets.ApiGateway(api)),
+  });
+
+  // THEN
+  expectStack(stack).to(haveResource('AWS::Route53::RecordSet', {
+    Name: 'example.com.',
+    Type: 'A',
+    AliasTarget: {
+      DNSName: {
+        'Fn::GetAtt': [
+          'apiCustomDomain64773C4F',
+          'RegionalDomainName',
+        ],
+      },
+      HostedZoneId: {
+        'Fn::GetAtt': [
+          'apiCustomDomain64773C4F',
+          'RegionalHostedZoneId',
+        ],
+      },
+    },
+    HostedZoneId: {
+      Ref: 'zoneEB40FF1E',
+    },
+  }));
+});