fix(region-info): integ use standalone package (#34782)

### Issue # (if applicable)

Closes #34692

### Reason for this change



### Description of changes
- Modify `integ.elastic-beanstalk-hostedzoneid` to use standalone `@aws-cdk/region-info`. We still have `integ.elastic-beanstalk-environment-target` using monolithic one
- Remove duplicate exports https://github.com/aws/aws-cdk/blob/1ae14635cbbc8ba0f2dab8cbeb72c4af0fddce7a/packages/aws-cdk-lib/package.json#L507-L511

### Describe any new or updated permissions being added




### Description of how you validated changes
Reproducing:
1. Change integ to use standalone `@aws-cdk/region-info`
2. Build integ
3. Remove export in `packages/aws-cdk-lib/package.json`
4. Build aws-cdk-lib
5. Run integ > error
```console
$ yarn integ test/aws-route53-targets/test/integ.elastic-beanstalk-hostedzoneid.js
yarn run v1.22.22
$ integ-runner --language javascript test/aws-route53-targets/test/integ.elastic-beanstalk-hostedzoneid.js

Verifying integration test snapshots...

node:internal/modules/cjs/loader:641
      throw e;
      ^

Error [ERR_PACKAGE_PATH_NOT_EXPORTED]: Package subpath './core/lib/errors' is not defined by "exports" in /workspaces/aws-cdk/node_modules/aws-cdk-lib/package.json
    at exportsNotFound (node:internal/modules/esm/resolve:322:10)
    at packageExportsResolve (node:internal/modules/esm/resolve:670:9)
    at resolveExports (node:internal/modules/cjs/loader:634:36)
    at Module._findPath (node:internal/modules/cjs/loader:724:31)
    at Module._resolveFilename (node:internal/modules/cjs/loader:1211:27)
    at Module._load (node:internal/modules/cjs/loader:1051:27)
    at Module.require (node:internal/modules/cjs/loader:1311:19)
    at require (node:internal/modules/helpers:179:18)
    at Object.<anonymous> (/workspaces/aws-cdk/packages/@aws-cdk/region-info/lib/fact.js:8:18)
    at Module._compile (node:internal/modules/cjs/loader:1469:14) {
  code: 'ERR_PACKAGE_PATH_NOT_EXPORTED'
}

Node.js v20.18.3
```

### 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: phuhung273

packages/@aws-cdk-testing/framework-integ/package.json

@@ -47,6 +47,7 @@
     "@aws-cdk/lambda-layer-kubectl-v31": "^2.1.0",
     "@aws-cdk/lambda-layer-kubectl-v32": "^2.1.0",
     "@aws-cdk/lambda-layer-kubectl-v33": "^2.0.0",
+    "@aws-cdk/region-info": "0.0.0",
     "aws-cdk-lib": "0.0.0",
     "cdk8s": "2.69.74",
     "cdk8s-plus-27": "2.9.5",

packages/@aws-cdk-testing/framework-integ/test/aws-route53-targets/test/integ.elastic-beanstalk-hostedzoneid.ts

@@ -6,7 +6,7 @@ import * as targets from 'aws-cdk-lib/aws-route53-targets';
 import { IntegTest } from '@aws-cdk/integ-tests-alpha';
 import * as elasticbeanstalk from 'aws-cdk-lib/aws-elasticbeanstalk';
 import * as custom from 'aws-cdk-lib/custom-resources';
-import { RegionInfo } from 'aws-cdk-lib/region-info';
+import { RegionInfo } from '@aws-cdk/region-info';
 
 const app = new App({
   postCliContext: {