fix(scheduler): the value of the description property is not reflecte…

…d to the resource. (#31276)

### Issue # (if applicable)

Closes #31269 .

### Reason for this change
The `description` property is not used in the `Schedule` class.
As a result, the value of the `description` property is not reflected to the resource.



### Description of changes
Modify to set the value of props to the `description` property.



### Description of how you validated changes
Add a unit test and an integ 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-scheduler-alpha/lib/schedule.ts

@@ -352,6 +352,7 @@ export class Schedule extends Resource implements ISchedule {
       },
       startDate: props.start?.toISOString(),
       endDate: props.end?.toISOString(),
+      description: props.description,
     });
 
     this.scheduleName = this.getResourceNameAttribute(resource.ref);

packages/@aws-cdk/aws-scheduler-alpha/test/integ.schedule.js.snapshot/aws-cdk-scheduler-schedule.template.json

@@ -411,6 +411,37 @@
      }
     }
    }
+  },
+  "UseDescription170B07AB": {
+   "Type": "AWS::Scheduler::Schedule",
+   "Properties": {
+    "Description": "test description",
+    "FlexibleTimeWindow": {
+     "Mode": "OFF"
+    },
+    "ScheduleExpression": "rate(12 hours)",
+    "ScheduleExpressionTimezone": "Etc/UTC",
+    "State": "ENABLED",
+    "Target": {
+     "Arn": {
+      "Fn::GetAtt": [
+       "Function76856677",
+       "Arn"
+      ]
+     },
+     "Input": "\"Input Text\"",
+     "RetryPolicy": {
+      "MaximumEventAgeInSeconds": 180,
+      "MaximumRetryAttempts": 3
+     },
+     "RoleArn": {
+      "Fn::GetAtt": [
+       "Role1ABCC5F0",
+       "Arn"
+      ]
+     }
+    }
+   }
   }
  },
  "Parameters": {

packages/@aws-cdk/aws-scheduler-alpha/test/integ.schedule.ts

@@ -104,6 +104,12 @@ new scheduler.Schedule(stack, 'ScheduleWithTimeFrame', {
   end: new Date(`${currentYear + 2}-10-01T00:00:00.000Z`),
 });
 
+new scheduler.Schedule(stack, 'UseDescription', {
+  schedule: expression,
+  target: target,
+  description: 'test description',
+});
+
 new IntegTest(app, 'integtest-schedule', {
   testCases: [stack],
 });

packages/@aws-cdk/aws-scheduler-alpha/test/schedule.test.ts

@@ -214,5 +214,19 @@ describe('Schedule', () => {
         });
       }).toThrow('The provided duration must be between 1 minute and 1440 minutes, got 0');
     });
+
+    test('schedule with description', () => {
+      // WHEN
+      new Schedule(stack, 'TestSchedule', {
+        schedule: expr,
+        target: new SomeLambdaTarget(func, role),
+        description: 'test description',
+      });
+
+      // THEN
+      Template.fromStack(stack).hasResourceProperties('AWS::Scheduler::Schedule', {
+        Description: 'test description',
+      });
+    });
   });
 });