[CI Failure] Flaky: PRScriptShellTests.MockGhApiWorkflowWithoutJqFailsLoudly fails with 'Text file busy' race condition

## Build Information

Build: https://github.com/microsoft/aspire/actions/runs/29122927133
Build error leg or test failing: Tests / Acquisition / Acquisition (ubuntu-latest) / `Aspire.Acquisition.Tests.Scripts.PRScriptShellTests.MockGhApiWorkflowWithoutJqFailsLoudly`
Pull request: #18692

## Error Message

```
System.ComponentModel.Win32Exception : An error occurred trying to start process '/tmp/aspire-test-.../mock-bin/gh' ... Text file busy
at System.Diagnostics.Process.ForkAndExecProcess
at Aspire.Acquisition.Tests.Scripts.PRScriptShellTests.MockGhApiWorkflowWithoutJqFailsLoudly()
```

## Description

Flaky: PRScriptShellTests.MockGhApiWorkflowWithoutJqFailsLoudly fails with 'Text file busy' race condition

**Type**: flaky-test

## Occurrences

| Date | Build | Job | PR |
|------|-------|-----|----|
| 2026-07-11 | [29122927133](https://github.com/microsoft/aspire/actions/runs/29122927133) | Tests / Acquisition / Acquisition (ubuntu-latest) | #18692 |
| 2026-08-21 | [32529484553](https://github.com/microsoft/aspire/actions/runs/32529484553) | Tests / Acquisition / Acquisition (ubuntu-latest) | #19559 |

Start with Aspire.Acquisition.Tests.Scripts.PRScriptShellTests.MockGhApiWorkflowWithoutJqFailsLoudly and reproduce it from the linked Acquisition Ubuntu build. Trace the mocked gh process setup around the reported Text file busy error; done means the test reliably passes without the race condition.

Written by the indexing model from the issue text.