chore: fix duplicate word typos in alpha packages and custom resource handlers

Fix repeated words in comments:
- "the the" → "the" (4 occurrences)
- "an an" → "an" (1 occurrence)

Author: syukawa-dev

packages/@aws-cdk/app-staging-synthesizer-alpha/lib/staging-stack.ts

@@ -82,7 +82,7 @@ export interface IStagingResourcesFactory {
   /**
    * Return an object that will manage staging resources for the given stack
    *
-   * This is called whenever the the `AppStagingSynthesizer` binds to a specific
+   * This is called whenever the `AppStagingSynthesizer` binds to a specific
    * stack, and allows selecting where the staging resources go.
    *
    * This method can choose to either create a new construct (perhaps a stack)

packages/@aws-cdk/custom-resource-handlers/lib/aws-route53/cross-account-zone-delegation-handler/index.ts

@@ -106,7 +106,7 @@ async function getHostedZoneIdByName(name: string, route53: Route53): Promise<st
  * By default, STS AssumeRole will call the STS endpoint for the same region
  * as the Lambda runs in. Normally, this is all good. However, when the AssumeRole
  * is used to assume a role in a different account A, the AssumeRole will fail if the
- * Lambda is executing in an an opt-in region R to which account A has not been opted in.
+ * Lambda is executing in an opt-in region R to which account A has not been opted in.
  *
  * To solve this, we will always AssumeRole in the same region as the Route53 call will
  * resolve to.

packages/@aws-cdk/custom-resource-handlers/lib/core/cross-region-ssm-writer-handler/index.ts

@@ -157,7 +157,7 @@ function except(source: CrossRegionExports, filter: CrossRegionExports): CrossRe
 }
 
 /**
- * Return items that exist in both the the old parameters and the new parameters,
+ * Return items that exist in both the old parameters and the new parameters,
  * but have different values
  *
  * @param oldParams the exports that existed previous to this execution

packages/@aws-cdk/integ-tests-alpha/lib/assertions/api-call-base.ts

@@ -11,7 +11,7 @@ import type { WaiterStateMachineOptions } from './waiter-state-machine';
 export interface IApiCall extends IConstruct {
   /**
    * access the AssertionsProvider. This can be used to add additional IAM policies
-   * the the provider role policy
+   * the provider role policy
    *
    * @example
    * declare const apiCall: AwsApiCall;

packages/@aws-cdk/integ-tests-alpha/lib/assertions/sdk.ts

@@ -56,7 +56,7 @@ export class AwsApiCall extends ApiCallBase {
   /**
    * access the AssertionsProvider for the waiter state machine.
    * This can be used to add additional IAM policies
-   * the the provider role policy
+   * the provider role policy
    *
    * @example
    * declare const apiCall: AwsApiCall;