[NETE2ESDK][LLM][Intermittent] The uninstaller of .NET SDK have been blocked by another progress.

### Describe the bug.

When ask agent to uninstall .net sdk, it reports error that the uninstaller may have been cancelled, blocked by another progress.

### Please attach log file(s) here if you have any.

[Log.zip](https://github.com/user-attachments/files/28786104/20260610T155813.zip)

### Reproduction Steps

1. On windows x64, login VSCode with your GitHub Account to enable usage of CoPilot
2. Ask the agent in the chat window to install .NET sdk 10.0.301
3. Ask the agent in the chat window to uninstall .NET sdk 10.0.301

**Note**: This issue repro after we finish some testing, and we don't know which action due to it occurred.

### Expected Behavior

.NET SDK can be uninstalled successfully.

### Exceptions & Errors (if any)

.NET SDK can't be uninstalled

### .NET Install Tool Version

3.1.0

### Your operating system? Please provide more detail, such as the version and or distro above.

N/A

### VS Code Version

1.123.1