[CI Failure] Flaky: VS Code extension E2E (Windows, apphost-lifecycle-tools) shard fails, unrelated to PR changes

## Build Information

Build: https://github.com/microsoft/aspire/actions/runs/31762325235
Build error leg: Tests / Dashboard / Dashboard (ubuntu-latest)
Pull request: #19371

## Error Message

```
Process completed with exit code 1. (Run extension E2E tests step failed; detailed job logs unavailable)
```

## Description

Flaky: VS Code extension E2E (Windows, apphost-lifecycle-tools) shard fails, unrelated to PR changes

**Type**: flaky-test

## Occurrences

| Date | Build | Job | PR |
|------|-------|-----|----|
| 2026-08-14 | [31762325235](https://github.com/microsoft/aspire/actions/runs/31762325235) | Tests / Dashboard / Dashboard (ubuntu-latest) | #19371 |
| 2026-08-26 | [32997866203](https://github.com/microsoft/aspire/actions/runs/32997866203) | Tests / Run VS Code extension E2E tests / VS Code extension E2E (Windows, apphost-lifecycle-tools) | #19705 |

Start with the linked workflow runs 31762325235 and 32997866203, focusing on the VS Code extension E2E Windows apphost-lifecycle-tools shard. Compare the failed jobs and rerun results, since detailed logs are unavailable for the first run. Done means identifying the flaky failure and making the shard reliably pass without depending on unrelated PR changes.

Written by the indexing model from the issue text.