(@aws-cdk/integ-tests-alpha): (spawnSync cdk ENOENT on Windows)

### Describe the bug

When running the integ-test module on a Windows 11 machine the following error gets logged:

`Integration test failed: Error: spawnSync cdk ENOENT`

I have attempted this on two Windows 11 machines, both having Docker and esbuild installed, as well as the windows-latest running on Github Actions.

I have also tested running it on an Ubuntu-based Github action, as well as running it with WSL, where the error is not present either.

_See this discussion for another person having the same issue https://github.com/aws/aws-cdk/discussions/25274_

### Expected Behavior

The IntegTest running as it does on a Linux machine.

### Current Behavior

```
> cdk-integ-tests-sample@0.1.0 integ-test D:\a\cdk-integ-tests-sample\cdk-integ-tests-sample
> integ-runner --directory ./integ-tests --parallel-regions us-east-1 --update-on-failed

Verifying integration test snapshots...

NEW integ.sns-sqs-ddb 4.051s

Snapshot Results:

Tests: 1 failed, 1 total

Running integration tests for failed tests...

Running in parallel across regions: us-east-1
Running test D:\a\cdk-integ-tests-sample\cdk-integ-tests-sample\integ-tests\integ.sns-sqs-ddb.js in us-east-1
FAILED integ.sns-sqs-ddb-DataFlowTest/DefaultTest (undefined/us-east-1) 3.533s
Integration test failed: Error: spawnSync cdk ENOENT

Test Results:

Tests: 1 failed, 1 total
Error: Some integration tests failed!
at main (D:\a\cdk-integ-tests-sample\cdk-integ-tests-sample\node_modules\@aws-cdk\integ-runner\lib\index.js:1036[7](https://github.com/MaximilianSchon/cdk-integ-tests-sample/actions/runs/5061372221/jobs/9085491934#step:6:8):[15](https://github.com/MaximilianSchon/cdk-integ-tests-sample/actions/runs/5061372221/jobs/9085491934#step:6:16))
```

### Reproduction Steps

https://github.com/MaximilianSchon/cdk-integ-tests-sample

See Github Action for execution.

### Possible Solution

_No response_

### Additional Information/Context

_No response_

### CDK CLI Version

2.7.8

### Framework Version

_No response_

### Node.js Version

v16.6.1

### OS

Windows (11)

### Language

Typescript

### Language Version

_No response_

### Other information

_No response_

Start at the integ-runner entry point shown in node_modules/@aws-cdk/integ-runner/lib/index.js:1036 and reproduce the sample repository's Windows GitHub Action failure. Compare the Windows and Ubuntu runs around the `spawnSync cdk ENOENT` error; done means the integ test completes successfully on Windows as it does on Linux.

Written by the indexing model from the issue text.