[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.

Start by reproducing the failure from the Claude desktop Code tab using mcp__Claude_Browser__navigate and the provided diagnostics. Compare the session's detected MCP names with the configured servers; done means the built-in Browser pane actions execute without the false reserved-name conflict.

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