[NETE2ESDK][Linux][LLM]It should NOT suggest `dotnet.existingDotnetPath` if ask agent which custom .net installed and how to use it on Linux

### Describe the bug.

It should NOT suggest `dotnet.existingDotnetPath` if ask agent which custom .net installed and how to use it on Linux

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

[logs.zip](https://github.com/user-attachments/files/28632525/logs.zip)

### Reproduction Steps

1. On Ubuntu 26.04 , download and extract dotnet-sdk-10.0.300-linux-x64.tar.gz and add to paths
2. login VSCode with your GitHub Account to enable usage of CoPilot
3. Ask the agent in the chat window to which custom .net installed, then ask how to use my custom .net install
4. Observe

### Expected Behavior

It should NOT suggest `dotnet.existingDotnetPath` as that only controls private runtime installs.

### Exceptions & Errors (if any)

It suggests `dotnet.existingDotnetPath`

### .NET Install Tool Version

3.1.0-b

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

Linux

### VS Code Version

v1.122.1