LSP server not found when configured via project-level .github/lsp.json

### Describe the bug

GitHub Copilot CLI fails to locate or initialize LSP servers when they are defined in a project-specific `.github/lsp.json` file, even though the CLI correctly detects the file's presence. The same configuration works perfectly when placed in the global `~/.copilot/lsp-config.json`.

Not working example in `.github/lsp.json`
```
/lsp

LSP Server Status:
Project-configured servers:
• typescript: (.ts, .tsx)

User config: C:\Users\user\.copilot\lsp-config.json
Project config: C:\project\.github\lsp.json
```

```
/lsp test typescript
✗ Server "typescript" not found. Available: (none)
```
Lsp works correctly if cofigured in: `.~/.copilot/lsp-config.json`.

```
User-configured servers:
• typescript: typescript-language-server (.ts, .tsx)

User config: C:\Users\user\.copilot\lsp-config.json

 ✓ Server "typescript" started successfully!

PID: 24812
Spawn time: 20ms

Server was killed after successful test.
```

### Affected version

1.0.12

### Steps to reproduce the behavior

1. Configure lsp in `.github/lsp.json`
2. Start copilot
3. /lsp test lsp-name

### Expected behavior

LSP server should start successfully.

### Additional context

Used config:
```
{
"lspServers": {
"typescript": {
"command": "typescript-language-server",
"args": ["--stdio"],
"fileExtensions": {
".ts": "typescript",
".tsx": "typescript"
}
}
}
}
```

Windows 11, Terminal, Powershell7

Start with the project configuration path in .github/lsp.json and compare it with the working ~/.copilot/lsp-config.json path. Reproduce the issue with /lsp test typescript on Windows, then verify that the project-configured typescript server starts successfully and reports the same status as the user-configured server.

Written by the indexing model from the issue text.