Copilot Chat requests intermittently fail with 400/500 errors when Datadog MCP is enabled

Title: Copilot Chat requests intermittently fail with 400/500 errors when Datadog MCP is enabled

Body:
Hi team,

I’m seeing intermittent failures in Copilot Chat / VS Code Insiders when using the agent workflow. The failures appear as either:

- `Reason: Request Failed: 400 ... invalid_request_body` with a schema error mentioning `client_group_by` / `server_group_by`
- `Reason: Server error: 500`

Environment details:
- VS Code Insiders version: `1.133.0-insider` (observed in local debug logs)
- GitHub Copilot Chat extension version: `0.61.2026080705` (from local session logs)
- Datadog MCP plugin version: `0.7.15`
- Datadog plugin source: local VS Code agent plugin at `github.com/datadog-labs/vscode-plugin`

Observed behavior:
- The issue appears intermittently in new chats.
- The earlier failure was specifically rejected by the tool schema layer with a message indicating the request body used an unsupported JSON schema pattern (`client_group_by` / `server_group_by`).
- A later failing request returned a generic `500` from the service.

This looks like a Copilot/agent-tooling regression rather than a workspace-code issue. The failures occur even in new chats and are consistent with the Datadog MCP tool integration being involved.

Steps to reproduce:
1. Open VS Code Insiders with the GitHub Copilot Chat extension enabled.
2. Enable the Datadog MCP plugin / agent tool.
3. Trigger a Copilot Chat request in a new chat.
4. Intermittently, the request fails with either the 400 schema error or a generic 500 backend error.

Request IDs observed:
- `Client Request Id: 645bbea5-aabd-4c5f-94e9-e06459890326`
- `GH Request Id: 06C8:2FAEE9:F7638:110EDC:6A7A1B68`
- `Client Request Id: 6222a924-9e0e-4378-b419-27a44693b230`
- `GH Request Id: 5C93:126EE5:499395:4FAB07:6A7B27A4`

Thanks,