[BUG] Built-in Browser pane tool fails with false "reserved MCP name" conflict error

### Preflight Checklist

- [x] I have searched [existing issues](https://github.com/anthropics/claude-code/issues?q=is%3Aissue%20state%3Aopen%20label%3Abug) and this hasn't been reported yet
- [x] This is a single bug report (please file separate reports for different bugs)
- [x] I am using the latest version of Claude Code

### What's Wrong?

The built-in Browser pane tool (mcp__Claude_Browser__*) fails on every call with:

"An MCP server in this session ("Claude Browser") uses a name reserved for the desktop app's built-in tools, so this tool is unavailable here. Rename or remove that server in your MCP configuration, then start a new session."

This happens even though no MCP server named "Claude Browser" exists in any configuration (see diagnostics below). Reproduced across multiple separate sessions.

### What Should Happen?

The Browser pane tool should execute the navigate/computer action normally, without any "reserved MCP server name" error, since no such MCP server exists in the configuration.

### Error Messages/Logs

```shell
An MCP server in this session ("Claude Browser") uses a name reserved for the desktop app's built-in tools, so this tool is unavailable here. Rename or remove that server in your MCP configuration, then start a new session.
```

### Steps to Reproduce

1. Open Claude desktop app, start a new session.
2. Ask Claude to open any URL using the built-in Browser pane (e.g. "open https://example.com in the browser").
3. Claude calls the Browser tool (mcp__Claude_Browser__navigate or similar).
4. The call immediately fails with: "An MCP server in this session ("Claude Browser") uses a name reserved for the desktop app's built-in tools, so this tool is unavailable here. Rename or remove that server in your MCP configuration, then start a new session."

Diagnostics performed — no conflicting MCP server actually exists:
- Settings → Connectors: no connector named "Claude Browser" (only "Claude in Chrome" is listed, type Desktop/Included).
- ~/.claude.json: no mcpServers entry named "Claude Browser" at user or project scope.
- ~/Library/Application Support/Claude/claude_desktop_config.json: no mcpServers key at all.
- No installed plugins define such a server.
- `claude mcp list` (CLI): "No MCP servers configured."

Reproduced across multiple separate sessions, not a one-off.

### Claude Model

None

### Is this a regression?

I don't know

### Last Working Version

_No response_

### Claude Code Version

2.1.220 (Claude Code)

### Platform

Anthropic API

### Operating System

macOS

### Terminal/Shell

Terminal.app (macOS)

### Additional Information

This bug occurs in the Claude desktop app (Code tab), not in a raw terminal claude session — the failing tool is the app's built-in Browser pane (in-app preview browser), not something invoked from the shell.

Screenshot of the underlying error and the Connectors settings page (showing no "Claude Browser" connector exists) available on request.