feat(logs): add distribution property to the Subscription class (#30423)

### Issue # (if applicable)

Closes #30422

### Reason for this change
Missing Property in the Subscription class.



### Description of changes
Add destination property to the Subscription class.



### Description of how you validated changes
Add unit tests and integ tests.



### 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-testing/framework-integ/test/aws-logs/test/integ.subscriptionfilter-distribution.js.snapshot/aws-cdk-subscriptionfilter-distribution-integ.template.json

@@ -0,0 +1,172 @@
+{
+ "Resources": {
+  "LogGroupF5B46931": {
+   "Type": "AWS::Logs::LogGroup",
+   "Properties": {
+    "RetentionInDays": 731
+   },
+   "UpdateReplacePolicy": "Retain",
+   "DeletionPolicy": "Retain"
+  },
+  "LogGroupSubscriptionCloudWatchLogsCanPutRecords29011851": {
+   "Type": "AWS::IAM::Role",
+   "Properties": {
+    "AssumeRolePolicyDocument": {
+     "Statement": [
+      {
+       "Action": "sts:AssumeRole",
+       "Effect": "Allow",
+       "Principal": {
+        "Service": "logs.amazonaws.com"
+       }
+      }
+     ],
+     "Version": "2012-10-17"
+    }
+   }
+  },
+  "LogGroupSubscriptionCloudWatchLogsCanPutRecordsDefaultPolicyB7125314": {
+   "Type": "AWS::IAM::Policy",
+   "Properties": {
+    "PolicyDocument": {
+     "Statement": [
+      {
+       "Action": [
+        "kinesis:ListShards",
+        "kinesis:PutRecord",
+        "kinesis:PutRecords"
+       ],
+       "Effect": "Allow",
+       "Resource": {
+        "Fn::GetAtt": [
+         "Stream790BDEE4",
+         "Arn"
+        ]
+       }
+      },
+      {
+       "Action": "iam:PassRole",
+       "Effect": "Allow",
+       "Resource": {
+        "Fn::GetAtt": [
+         "LogGroupSubscriptionCloudWatchLogsCanPutRecords29011851",
+         "Arn"
+        ]
+       }
+      }
+     ],
+     "Version": "2012-10-17"
+    },
+    "PolicyName": "LogGroupSubscriptionCloudWatchLogsCanPutRecordsDefaultPolicyB7125314",
+    "Roles": [
+     {
+      "Ref": "LogGroupSubscriptionCloudWatchLogsCanPutRecords29011851"
+     }
+    ]
+   }
+  },
+  "LogGroupSubscriptionE3573E29": {
+   "Type": "AWS::Logs::SubscriptionFilter",
+   "Properties": {
+    "DestinationArn": {
+     "Fn::GetAtt": [
+      "Stream790BDEE4",
+      "Arn"
+     ]
+    },
+    "Distribution": "Random",
+    "FilterName": "CustomSubscriptionFilterName",
+    "FilterPattern": "\"ERROR\" \"MainThread\"",
+    "LogGroupName": {
+     "Ref": "LogGroupF5B46931"
+    },
+    "RoleArn": {
+     "Fn::GetAtt": [
+      "LogGroupSubscriptionCloudWatchLogsCanPutRecords29011851",
+      "Arn"
+     ]
+    }
+   },
+   "DependsOn": [
+    "LogGroupSubscriptionCloudWatchLogsCanPutRecordsDefaultPolicyB7125314"
+   ]
+  },
+  "Stream790BDEE4": {
+   "Type": "AWS::Kinesis::Stream",
+   "Properties": {
+    "RetentionPeriodHours": 24,
+    "ShardCount": 1,
+    "StreamEncryption": {
+     "Fn::If": [
+      "AwsCdkKinesisEncryptedStreamsUnsupportedRegions",
+      {
+       "Ref": "AWS::NoValue"
+      },
+      {
+       "EncryptionType": "KMS",
+       "KeyId": "alias/aws/kinesis"
+      }
+     ]
+    }
+   },
+   "UpdateReplacePolicy": "Retain",
+   "DeletionPolicy": "Retain"
+  }
+ },
+ "Conditions": {
+  "AwsCdkKinesisEncryptedStreamsUnsupportedRegions": {
+   "Fn::Or": [
+    {
+     "Fn::Equals": [
+      {
+       "Ref": "AWS::Region"
+      },
+      "cn-north-1"
+     ]
+    },
+    {
+     "Fn::Equals": [
+      {
+       "Ref": "AWS::Region"
+      },
+      "cn-northwest-1"
+     ]
+    }
+   ]
+  }
+ },
+ "Parameters": {
+  "BootstrapVersion": {
+   "Type": "AWS::SSM::Parameter::Value<String>",
+   "Default": "/cdk-bootstrap/hnb659fds/version",
+   "Description": "Version of the CDK Bootstrap resources in this environment, automatically retrieved from SSM Parameter Store. [cdk:skip]"
+  }
+ },
+ "Rules": {
+  "CheckBootstrapVersion": {
+   "Assertions": [
+    {
+     "Assert": {
+      "Fn::Not": [
+       {
+        "Fn::Contains": [
+         [
+          "1",
+          "2",
+          "3",
+          "4",
+          "5"
+         ],
+         {
+          "Ref": "BootstrapVersion"
+         }
+        ]
+       }
+      ]
+     },
+     "AssertDescription": "CDK bootstrap stack version 6 required. Please run 'cdk bootstrap' with a recent version of the CDK CLI."
+    }
+   ]
+  }
+ }
+}