fix(region-info): integ use standalone package

[phuhung273]

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

  aws-cdk/packages/aws-cdk-lib/package.json

  Lines 507 to 511 in 1ae1463

  	"./core/lib/errors": "./core/lib/errors.js",
  	"./core/lib/helpers-internal": "./core/lib/helpers-internal/index.js",
  	"./core/lib/metadata-resource": "./core/lib/metadata-resource.js",
  	"./core/lib/prop-injectable": "./core/lib/prop-injectable.js",
  	"./core/lib/errors": "./core/lib/errors.js",

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

$ 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

• My code adheres to the CONTRIBUTING GUIDE and DESIGN GUIDELINES

---

By submitting this pull request, I confirm that my contribution is made under the terms of the Apache-2.0 license

[aws-cdk-automation]

The pull request linter fails with the following errors:

❌ Fixes must contain a change to an integration test file and the resulting snapshot.

If you believe this pull request should receive an exemption, please comment and provide a justification. A comment requesting an exemption should contain the text Exemption Request. Additionally, if clarification is needed, add Clarification Request to a comment.

✅ A exemption request has been requested. Please wait for a maintainer's review.

[phuhung273]

Exemption Request: no need snapshot change

[aws-cdk-automation]

AWS CodeBuild CI Report

• CodeBuild project: AutoBuildv2Project1C6BFA3F-wQm2hXv2jqQv
• Commit ID: e9aeac0
• Result: SUCCEEDED
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