[FEATURE] Desktop app: let users choose which panel buttons are pinned in the session toolbar vs. hidden in the "⋮" menu

### Preflight Checklist

- [X] I have searched [existing requests](https://github.com/anthropics/claude-code/issues?q=is%3Aissue%20label%3Aenhancement) and this feature hasn't been requested yet
- [X] This is a single feature request (not multiple features)

### Problem Statement

In the desktop app's Code tab, the top-right toolbar of a session shows a fixed set of buttons: Terminal, the file/side pane, Browser, and a "⋮" overflow menu. Everything else, including Background tasks, lives behind the overflow menu.

Which buttons are pinned and which are hidden is hardcoded. There is no setting, drag-to-pin, or right-click option to change it, and nothing in `config.json`, `claude_desktop_config.json`, `~/.claude/settings.json`, or `keybindings.json` affects the toolbar.

I run background agents and subagents in most sessions, so I open the Background tasks panel far more often than the Terminal or Browser pane. Every time that is two clicks (⋮ then Background tasks) instead of one, and the panel has no keyboard shortcut either (`/tasks` only prints a list in the chat). Other people will have a different "most used" panel, which is exactly why this should be user-configurable rather than a different fixed default.

### Proposed Solution

Let the user choose which panel buttons are pinned in the session toolbar and which go into the "⋮" overflow menu. Any of these would work, roughly in order of preference:

1. **Right-click on a toolbar button or on an entry in the ⋮ menu** with "Pin to toolbar" / "Move to overflow menu". Order of pinned items could follow the order they were pinned in, or allow drag to reorder.
2. **A "Customize toolbar" entry in the ⋮ menu** that opens a small checklist of the available panels (Terminal, Files, Browser, Background tasks, Artifacts, ...) with a pinned/hidden toggle for each.
3. **A settings key**, so the layout can be versioned and shared across machines, for example in `~/.claude/settings.json`:

```json
{
"desktop": {
"sessionToolbar": ["backgroundTasks", "terminal", "browser"]
}
}
```

Anything not listed would fall into the overflow menu. The setting should apply to new sessions by default, so I do not have to re-pin per session.

### Alternative Solutions

- Opening it through ⋮ → Background tasks every time. Works, but it is the panel I use most and it is the one that is hidden.
- Typing `/tasks` in the session. That only prints the task list into the chat, it does not open the panel.
- Looked for a config knob: checked the desktop app's `config.json` and `claude_desktop_config.json`, `~/.claude/settings.json`, `~/.claude/keybindings.json`, and the app's Local Storage. None of them contain anything toolbar-related, and the main window UI is loaded remotely, so there is no local file to patch.
- Related but different: #73748 asks for user-added buttons that run custom commands or agents. This request is only about choosing which of the existing built-in panel buttons are pinned. The two could share the same configuration surface.

### Priority

Medium - Would be very helpful

### Feature Category

Configuration and settings

### Use Case Example

1. I start a session and delegate work to several subagents, so 3 or 4 background tasks are running.
2. I want to check their progress and switch between them, which means opening the Background tasks panel.
3. Today: click ⋮, then click Background tasks. Repeat every time I close the panel or open a new session.
4. With this feature: Background tasks is pinned as the first toolbar button and opens with one click, in every session, on every machine that shares my settings.

### Additional Context

- Claude desktop app 1.46388.4 (Microsoft Store / MSIX install), bundled Claude Code CLI 2.1.260
- Windows 11 Pro, build 10.0.26200
- Screenshot of the current toolbar: Terminal, side pane, Browser, "⋮". Background tasks is only reachable through "⋮".

- Precedent in other tools: VS Code lets you right-click editor title actions and the activity bar to hide, show, and reorder them; JetBrains has "Customize Toolbar" on right-click. Both persist the choice in settings so it follows the user.

The issue names the desktop app Code tab session toolbar, the ⋮ overflow menu, and settings files such as config.json, claude_desktop_config.json, ~/.claude/settings.json, and ~/.claude/keybindings.json. First find where the desktop toolbar and settings persistence are implemented. Done means users can choose which existing panel buttons are pinned vs overflow, and that choice applies to new sessions.

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