[NETE2ESDK][MAC][LLM] GitHub CoPilot can't find installed sdk or runtimes when first ask "what .net version installed".

### Describe the bug.

When first ask Agent with "what .net version installed", it can't find installed sdk or runtimes, but it can find after multiple attempts.

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

[Log.zip](https://github.com/user-attachments/files/28544452/20260603T165528.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 sdk 10.0.300
3. Ask the agent in the chat window with "what .net version installed"

### Expected Behavior

Installed sdk or runtime can be found.

### Exceptions & Errors (if any)

Installed sdk or runtime can't be found.

### .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