[NETE2ESDK][LLM] Support system level runtime installs with Agentic Tools

### Describe the bug.

When ask CoPilot to install runtime, it don't show the installing progress in output of .NET Install Tool.

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

[Log.zip](https://github.com/user-attachments/files/28500893/20260602T083454.zip)

### Reproduction Steps

1. Login VSCode with your GitHub Account to enable usage of CoPilot
2. Ask the agent in the chat window to install .NET Runtime 10.0.2

### Expected Behavior

The installing progress should appear in the output of .NET Install Tool.

### Exceptions & Errors (if any)

There is no installing progress show up in the output of .NET Install Tool, but show in 'dotnet --info'

### .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

1.122.1