[Failing test]: AspireNew_WithAgentInit_InstallsPlaywrightWithoutErrors

### Is there an existing issue for this?

- [x] I have searched the existing issues

### Build information

Build: https://github.com/microsoft/aspire/actions/runs/27591419958
Build error leg or test failing: `outerloop_tests / Cli.EndToEnd / Cli.EndToEnd (ubuntu-latest)` — `Aspire.Cli.EndToEnd.Tests.NewWithAgentInitTests.AspireNew_WithAgentInit_InstallsPlaywrightWithoutErrors`

### Error message

```json
{
"ErrorMessage": "Command failed with non-zero exit code (detected ERR prompt at sequence 12)",
"ErrorPattern": "",
"BuildRetry": false,
"ExcludeConsoleLog": false
}
```

### Error details

```yml
Error Message: System.InvalidOperationException : Command failed with non-zero exit code (detected ERR prompt at sequence 12). Check the terminal recording for details.
Stack Trace:
at Aspire.Tests.Shared.Hex1bAutomatorTestHelpers.WaitForSuccessPromptAsync(...) in tests/Shared/Hex1bAutomatorTestHelpers.cs:255
at Aspire.Cli.EndToEnd.Tests.NewWithAgentInitTests.AspireNew_WithAgentInit_InstallsPlaywrightWithoutErrors() in tests/Aspire.Cli.EndToEnd.Tests/NewWithAgentInitTests.cs:152
```

### Notes

This is an `[OuterloopTest]` and has failed **every scheduled Outerloop run this week (0/7)** — it is a deterministic, standing failure rather than flakiness. Surfaced by the weekly workflow-health report #18223.

A root-cause analysis (with the terminal recording excerpt and a suggested fix direction) is in a comment below.

📊 **[View CI Failure Report](https://github.com/microsoft/aspire/issues/18247#issuecomment-4722923929)**