chore(apigateway): fix the readme sections order. (#32650)

### Description of changes
Fixes the readme sections order to match the original order when `Breaking up Methods and Resources across Stacks` section was originally added in this PR #8270.  The current order does not make sense, this section does not related to the Step function backed rest API 

### 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-lib/aws-apigateway/README.md

@@ -12,9 +12,9 @@ running on AWS Lambda, or any web application.
 - [Amazon API Gateway Construct Library](#amazon-api-gateway-construct-library)
   - [Table of Contents](#table-of-contents)
   - [Defining APIs](#defining-apis)
+    - [Breaking up Methods and Resources across Stacks](#breaking-up-methods-and-resources-across-stacks)
   - [AWS Lambda-backed APIs](#aws-lambda-backed-apis)
   - [AWS StepFunctions backed APIs](#aws-stepfunctions-backed-apis)
-    - [Breaking up Methods and Resources across Stacks](#breaking-up-methods-and-resources-across-stacks)
   - [Integration Targets](#integration-targets)
   - [Usage Plan \& API Keys](#usage-plan--api-keys)
     - [Adding an API Key to an imported RestApi](#adding-an-api-key-to-an-imported-restapi)
@@ -76,6 +76,23 @@ const method = api.root.addResource('books').addMethod('GET');
 method.grantExecute(user);
 ```
 
+### Breaking up Methods and Resources across Stacks
+
+It is fairly common for REST APIs with a large number of Resources and Methods to hit the [CloudFormation
+limit](https://docs.aws.amazon.com/AWSCloudFormation/latest/UserGuide/cloudformation-limits.html) of 500 resources per
+stack.
+
+To help with this, Resources and Methods for the same REST API can be re-organized across multiple stacks. A common
+way to do this is to have a stack per Resource or groups of Resources, but this is not the only possible way.
+The following example uses sets up two Resources '/pets' and '/books' in separate stacks using nested stacks:
+
+[Resources grouped into nested stacks](test/integ.restapi-import.lit.ts)
+
+> **Warning:** In the code above, an API Gateway deployment is created during the initial CDK deployment.
+However, if there are changes to the resources in subsequent CDK deployments, a new API Gateway deployment is not
+automatically created. As a result, the latest state of the resources is not reflected. To ensure the latest state
+of the resources is reflected, a manual deployment of the API Gateway is required after the CDK deployment. See [Controlled triggering of deployments](#controlled-triggering-of-deployments) for more info.
+
 ## AWS Lambda-backed APIs
 
 A very common practice is to use Amazon API Gateway with AWS Lambda as the
@@ -255,23 +272,6 @@ AWS Step Functions will receive the following execution input:
 }
 ```
 
-### Breaking up Methods and Resources across Stacks
-
-It is fairly common for REST APIs with a large number of Resources and Methods to hit the [CloudFormation
-limit](https://docs.aws.amazon.com/AWSCloudFormation/latest/UserGuide/cloudformation-limits.html) of 500 resources per
-stack.
-
-To help with this, Resources and Methods for the same REST API can be re-organized across multiple stacks. A common
-way to do this is to have a stack per Resource or groups of Resources, but this is not the only possible way.
-The following example uses sets up two Resources '/pets' and '/books' in separate stacks using nested stacks:
-
-[Resources grouped into nested stacks](test/integ.restapi-import.lit.ts)
-
-> **Warning:** In the code above, an API Gateway deployment is created during the initial CDK deployment.
-However, if there are changes to the resources in subsequent CDK deployments, a new API Gateway deployment is not
-automatically created. As a result, the latest state of the resources is not reflected. To ensure the latest state
-of the resources is reflected, a manual deployment of the API Gateway is required after the CDK deployment. See [Controlled triggering of deployments](#controlled-triggering-of-deployments) for more info.
-
 ## Integration Targets
 
 Methods are associated with backend integrations, which are invoked when this