chore: update metadata_updater to skip some L2 constructs from being injectable (#34463)

### Issue # (if applicable)
N/A

### Reason for this change

Release was failing because when metadata_updater job got executed to automatically mark L2 constructs as injectables, it failed to update some constructs because they do not follow the normal patterns of L2 constructors. 

### Description of changes
 - Added skip logic to skip some L2 constructs from being marked as Injectables.
 - Applied the injectables logic manually to `RootResource` since it's constructor does not follow the common constructors pattern for L2s, and should support the injectable logic.
 - Skipped `lib/function-base.LatestVersion`, as in my opinion it does not need to support the injectable feature. The constructor does not accept any props, and so It does not support any injected property injection.
 - Added some changes to the metadata_updater tool itself to fix some linter errors.

### Description of how you validated changes

executed the metadata_updater job locally to verify the generated L2 constructs.

### 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*

Author: moelasmar

packages/aws-cdk-lib/aws-apigateway/lib/restapi.ts

@@ -21,6 +21,7 @@ import { ArnFormat, CfnOutput, IResource as IResourceBase, Resource, Stack, Toke
 import { ValidationError } from '../../core/lib/errors';
 import { addConstructMetadata, MethodMetadata } from '../../core/lib/metadata-resource';
 import { propertyInjectable } from '../../core/lib/prop-injectable';
+import { applyInjectors } from '../../core/lib/prop-injectors-helpers';
 import { APIGATEWAY_DISABLE_CLOUDWATCH_ROLE } from '../../cx-api';
 
 const RESTAPI_SYMBOL = Symbol.for('@aws-cdk/aws-apigateway.RestApiBase');
@@ -1140,6 +1141,7 @@ export enum RestApiMode {
 }
 
 class RootResource extends ResourceBase {
+  public static readonly PROPERTY_INJECTION_ID: string = 'aws-cdk-lib.aws-apigateway.RootResource';
   public readonly parentResource?: IResource;
   public readonly api: RestApiBase;
   public readonly resourceId: string;
@@ -1152,6 +1154,10 @@ class RootResource extends ResourceBase {
 
   constructor(api: RestApiBase, props: ResourceOptions, resourceId: string) {
     super(api, 'Default');
+    props = applyInjectors(RootResource.PROPERTY_INJECTION_ID, props, {
+      scope: api,
+      id: resourceId,
+    });
     // Enhanced CDK Analytics Telemetry
     addConstructMetadata(this, resourceId);
 

packages/aws-cdk-lib/core/lib/prop-injectable.ts

@@ -1,5 +1,5 @@
 import { Construct, IConstruct } from 'constructs';
-import { applyInjectors } from './private/prop-injectors-helpers';
+import { applyInjectors } from './prop-injectors-helpers';
 
 interface PropertyInjectableConstructConstructor {
   readonly PROPERTY_INJECTION_ID: string;

packages/aws-cdk-lib/core/lib/private/prop-injectors-helpers.ts renamed to packages/aws-cdk-lib/core/lib/prop-injectors-helpers.ts

@@ -1,5 +1,5 @@
 import { Construct, IConstruct, Node } from 'constructs';
-import { InjectionContext, IPropertyInjector, PropertyInjectors } from '../prop-injectors';
+import { InjectionContext, IPropertyInjector, PropertyInjectors } from './prop-injectors';
 
 /**
  * This symbol is needed to identify PropertyInjectors.

packages/aws-cdk-lib/core/lib/prop-injectors.ts

@@ -1,5 +1,5 @@
 import { Construct, IConstruct } from 'constructs';
-import { PROPERTY_INJECTORS_SYMBOL } from './private/prop-injectors-helpers';
+import { PROPERTY_INJECTORS_SYMBOL } from './prop-injectors-helpers';
 
 /**
  * This defines the values needed for Injection.

packages/aws-cdk-lib/core/test/prop-injectors.test.ts

@@ -1,9 +1,9 @@
 import { Construct } from 'constructs';
 import { Annotations, Resource, Stack, Stage } from '../lib';
 import { App } from '../lib/app';
-import { applyInjectors, findInjectorFromConstruct } from '../lib/private/prop-injectors-helpers';
 import { propertyInjectable } from '../lib/prop-injectable';
 import { InjectionContext, IPropertyInjector, PropertyInjectors } from '../lib/prop-injectors';
+import { applyInjectors, findInjectorFromConstruct } from '../lib/prop-injectors-helpers';
 
 // Define Injectors for our testing
 class DoNothingInjector implements IPropertyInjector {