fix: prevent infinite loop with self-referencing handoffs in Autopilot mode (#325128)

[AmariahAK]

Description

Fixes #325128

### What was the issue

In Autopilot mode, a custom agent with `handoffs` that have `send: true` pointing to the same agent creates an infinite loop. Each response auto-triggers a handoff back to itself, which produces the same response, which triggers the handoff again — forever.

### Where was the issue

`src/vs/workbench/contrib/chat/browser/widget/chatWidget.ts` — the `renderChatSuggestNextWidget()` method. When Autopilot is active and a response carries handoffs with `send: true`, the code auto-triggers the first matching handoff via `handleNextPromptSelection()` without checking whether the handoff targets the same mode that produced the response. The Copilot ToolCallingLoop correctly stops when the model produces a text-only response, but the handoff auto-trigger in the UI layer creates a new turn that restarts the cycle.

### How it was fixed

A single guard added at line 1351 in `renderChatSuggestNextWidget()`:

```diff
- if (autoSendHandoff) {
+ if (autoSendHandoff && autoSendHandoff.agent !== responseMode.name.get()) {

Before auto-triggering a send: true handoff, the code now compares the handoff's target agent against the name of the mode that produced the response. If they match (self-referencing), the auto-trigger is skipped. Handoff buttons are still rendered for manual use — only the automatic send is blocked for self-referencing handoffs.

Why this method over others

• Guard in the ToolCallingLoop: not viable — the loop has no visibility into handoffs, which live in the chat widget UI layer above it.
• Depth counter / cycle detector: over-engineered for a single equality check, adds state and complexity.
• Guard at the auto-trigger point (chosen): the fix lives exactly where the loop forms — minimal (1 condition), stateless, uses existing types (IHandOff.agent, IChatMode.name) already in scope. No new imports, no behavior change for legitimate cross-agent handoffs.

How to test

1. Create a .agent.md file with a self-referencing handoff:

   ---
   name: test agent
   description: 'A custom agent with handoffs.'
   tools: [vscode, execute, read, agent, edit, search, web, browser, todo]
   handoffs:
     - label: Button 1
       agent: 'test agent'
       prompt: This is a handoff from Button 1.
       send: true
     - label: Button 2
       agent: 'test agent'
       prompt: This is a handoff from Button 2.
       send: true
   ---
   Always reply with 'Hi, I'm your custom agent. How can I assist you today?'

2. Enable Autopilot mode and select the "test agent" mode

3. Send "Hi"

   • Before: infinite loop of auto-triggered handoffs
   • After: one response rendered, handoff buttons displayed, no auto-trigger

4. Verify handoff buttons are visible and clickable for manual use

5. Verify a Plan → Agent handoff with send: true still auto-triggers (different agents should work normally)

[Copilot]

Pull request overview

Prevents an infinite Autopilot loop in the chat widget when an agent response includes a self-referencing send: true handoff, by adding a guard before auto-triggering a handoff. This lives in the workbench chat UI layer (ChatWidget) where the auto-send behavior is implemented.

Changes:

• Add a condition to skip auto-triggering send: true handoffs that target the same agent/mode that produced the response.