[Remote] HTTP MCP Server Connection termination logs with VS Code Client

@vukelich is already working on this.

Since Oct 27, 2025.

## Issue Description

HTTP MCP server configuration in VS Code shows error logs reporting connection termination.

## Environment Information

**VS Code Version:**
```
1.105.1
7d842fb85a0275a4a8e4d7e040d2625abbf7f084
x64
```

**GitHub Copilot Extensions:**
```
github.copilot@1.388.0
github.copilot-chat@0.32.3
ms-azuretools.vscode-azure-github-copilot@1.0.137
```

**MCP Configuration:**
```json
{
"servers": {
"Azure MCP Server": {
"url": "http://localhost:1031/",
"type": "http"
}
},
"inputs": []
}
```

## Last Output Logs
```
2025-10-27 11:51:45.822 [info] Discovered 1 tools
2025-10-27 11:56:49.885 [info] Error reading from async stream, we will reconnect: TypeError: terminated
2025-10-27 11:56:50.905 [debug] 400 status connecting to http://localhost:1031/ for async notifications; they will be disabled: {"error":{"code":-32000,"message":"Bad Request: This server does not support multiple GET requests. Start a new session to get a new GET SSE response."},"id":"","jsonrpc":"2.0"}
```

## Steps to Reproduce

1. Configure MCP server with HTTP endpoint at `http://localhost:1031/`
2. Attempt to connect from VS Code client
3. Leave the VS code client idle for about 5 minutes to see the above log.

## Expected Behavior

No "errors" reported in the logs when there are none. This can be turned into a "debug" level log if this is only a internal connection management log. Doesn't need to be info message for the user.

## Actual Behavior
"Error reading from async stream, we will reconnect: TypeError: terminated" log as info to the user is not very useful and also not clear what "TypeError: terminated" means.

## Additional Context

- Running on Windows with PowerShell
- Local development environment
- Azure MCP server running on localhost:1031