[Bug]Custom agent appears duplicated in selection list and fails to load after restart

### Describe the bug

## Summary

When a custom agent's **filename** differs from its **frontmatter `name` field**, two issues occur:

1. The agent appears **duplicated** in the `/agent` selection menu (one entry from the filename, one from the `name` field).
2. After session restart, the CLI fails to find the previously selected agent with error: `Custom agent "xxx" not found`.

## Environment

- **GitHub Copilot CLI version**: v1.0.16-1
- **Model**: Claude Opus 4.6 (6x) (high)
- **OS**: Ubuntu 24.04.4 LTS (WSL2) on Windows
- **Kernel**: Linux 6.6.87.2-microsoft-standard-WSL2 aarch64
- **Node.js**: v24.14.0
- **Agent directory**: `~/.copilot/agents/`

## Agent Configuration

Two custom agent files exist in `~/.copilot/agents/`:

| File | Frontmatter `name` |
| ------------------ | ----------------------------- |
| `azure-expert.md` | `azure-solution-expert` |
| `azure-aws-doc.md` | `azure-vs-aws-compare-expert` |

Note: the **filename** and the **`name` field in frontmatter** are intentionally different.

## Steps to Reproduce

### Bug 1: Duplicate agent entry

1. Create a custom agent file at `~/.copilot/agents/azure-expert.md` with frontmatter `name: azure-solution-expert`
2. Start `ghcp`
3. Run `/agent` to open the agent selection menu

**Expected**: The agent should appear **once** in the list.

**Actual**: The agent appears **twice**:

```
Select Agent:
1. Default (deselect current agent)
> 2. azure-solution-expert (current)
3. azure-solution-expert · user <-- duplicate
4. azure-vs-aws-compare-expert · user
```

### Bug 2: Agent not found after restart

1. Select the custom agent `azure-solution-expert` via `/agent`
2. Restart the CLI session (close and reopen, or the session restarts automatically)

**Expected**: The agent should be loaded successfully on restart.

**Actual**: Error message on startup:

```
✗ Custom agent "azure-solution-expert" not found. Available agents: azure-aws-doc, azure-expert
● Environment loaded: 5 MCP servers, 1 skill, 2 agents
● Selected custom agent: azure-solution-expert
```

The "Available agents" list uses **filenames** (`azure-aws-doc`, `azure-expert`), but the persisted selection uses the **frontmatter `name`** (`azure-solution-expert`). The lookup fails because these don't match.

## Root Cause Analysis

The CLI appears to use **two different identifiers** for agents inconsistently:

- **Agent selection/persistence**: Uses the `name` field from the agent file's YAML frontmatter
- **Agent lookup on restart**: Uses the filename (without `.md` extension)

When filename ≠ frontmatter name, the agent:

- Gets registered under both identifiers → **duplicate in list**
- Gets persisted by frontmatter name but looked up by filename on restart → **not found error**

## Expected Behavior

1. The agent should appear **exactly once** in the selection list regardless of whether the filename matches the frontmatter `name` field.
2. The CLI should use a **consistent identifier** (either filename or frontmatter `name`, not both) for selection, persistence, and lookup.
3. If the frontmatter `name` takes priority over the filename, the persisted selection should resolve correctly on restart.

## Screenshot


## Workaround

Rename the agent file to match the frontmatter `name` field:

```bash
mv ~/.copilot/agents/azure-expert.md ~/.copilot/agents/azure-solution-expert.md
mv ~/.copilot/agents/azure-aws-doc.md ~/.copilot/agents/azure-vs-aws-compare-expert.md
```

## Labels

`bug`, `custom-agents`, `cli`

### Affected version

_No response_

### Steps to reproduce the behavior

_No response_

### Expected behavior

_No response_

### Additional context

_No response_

Bắt đầu bằng cách tái hiện vấn đề với một custom agent có tên tệp khác với tên trong frontmatter của nó, sau đó theo dõi quá trình phát hiện custom agent, lưu trạng thái lựa chọn và tra cứu khi khởi động lại. Công việc được hoàn tất khi agent xuất hiện đúng một lần trong /agent và cùng agent đã chọn được tải thành công sau khi CLI khởi động lại, không có lỗi not-found.

Do mô hình lập chỉ mục viết ra từ nội dung của issue.