[CI Failure] Flaky: VS Code extension E2E 'rediscovers workspace AppHost candidates when config changes' fails due to config file read/write race

## Build Information

Build: https://github.com/microsoft/aspire/actions/runs/31662686822
Build error leg or test failing: Tests / Run VS Code extension E2E tests / VS Code extension E2E (Linux, discovery-configuration) / `Aspire workspace discovery and configuration E2E rediscovers workspace AppHost candidates when config changes`
Pull request: #19178

## Error Message

```
assert.ok(multipleCandidates.state.workspaceAppHostCandidatePaths.length >= 2) evaluated to falsy. aspire config info stderr: The configuration file '.../aspire.config.json' contains invalid JSON: Expected depth to be zero at the end of the JSON payload. There is an open JSON object or array that should be closed. CLI AppHost discovery failed; using 1 AppHost project candidate(s) found in the workspace.
```

## Description

Flaky: VS Code extension E2E 'rediscovers workspace AppHost candidates when config changes' fails due to config file read/write race

**Type**: flaky-test

## Occurrences

| Date | Build | Job | PR |
|------|-------|-----|----|
| 2026-08-13 | [31662686822](https://github.com/microsoft/aspire/actions/runs/31662686822) | Tests / Run VS Code extension E2E tests / VS Code extension E2E (Linux, discovery-configuration) | #19178 |
| 2026-09-01 | [33555454691](https://github.com/microsoft/aspire/actions/runs/33555454691) | Tests / Run VS Code extension E2E tests / VS Code extension E2E (Windows, discovery-configuration) | #19846 |

Start with the VS Code extension E2E test named “rediscovers workspace AppHost candidates when config changes” and inspect the aspire.config.json read/write sequence around the discovery configuration flow. Reproduce the Linux or Windows discovery-configuration job, then verify the test consistently rediscovers at least two AppHost candidates without invalid-JSON errors.

Written by the indexing model from the issue text.