[BUG] Chrome integration unavailable in Remote Control sessions started by Desktop app

What's Wrong?

Chrome integration ("Claude in Chrome" MCP) is completely unavailable in Remote Control sessions started by the Claude Desktop app on Windows.

In Desktop app sessions: Chrome MCP tools (tabs_context_mcp, navigate, computer, etc.) work perfectly.
In Remote Control sessions (both from phone via claude.ai/code and from PC): Claude responds that Chrome MCP tools are not available. Only Windows-MCP, desktop-commander, and cloud connectors (Gmail, Calendar, etc.) are loaded.

The Remote Control documentation states: "your filesystem, MCP servers, tools, and project configuration all stay available." However, Chrome integration is not carried over to RC sessions.

Additionally, the /chrome command returns "Unknown skill: chrome" in the Desktop app, making it impossible to enable Chrome by default through the documented method.

Expected Behavior

Chrome integration should be available in Remote Control sessions.

Either:

1. The Desktop app should pass --chrome to the remote-control subprocess it spawns, OR
2. The /chrome command should work in Desktop app sessions to enable "Enabled by default" setting, OR
3. There should be a settings.json key to enable Chrome integration persistently across all session types

Error Output

• RC session: "Chrome MCP (mcp__Claude_in_Chrome__*) is not included in the available tools list."
• Desktop app /chrome: "Unknown skill: chrome"
• CLI claude remote-control --help: "Error: Remote Control requires a full-scope login token." (prevents starting own RC with --chrome)
• npx -y @anthropic-ai/chrome-mcp@latest: npm 404 (Chrome MCP is built-in, not an npm package)

Steps to Reproduce

1. Open Claude Desktop app (Windows, v1.569.0)
2. Desktop app starts claude remote-control --name ...
3. Connect from phone (claude.ai/code) or open the RC session on PC
4. Ask Claude to use Chrome MCP tools
5. Claude reports Chrome MCP is not available

Additional Context

Environment: Windows 11 Pro, Claude Desktop v1.569.0, CLI v2.1.85, Chrome extension installed (cachedChromeExtensionInstalled: true), Native messaging host registered.

Root cause analysis:

• Desktop app sessions use internal plugin mechanism (--plugin-dir flags) to load Chrome MCP
• Remote Control sessions spawned by Desktop app do NOT receive these flags
• Chrome MCP is NOT an npm package — it is a built-in feature, so .mcp.json configuration is impossible
• Cannot start remote-control from CLI independently (requires full-scope OAuth only available to Desktop app)
• The Desktop app's remote-control command claude.exe remote-control --name ... lacks --chrome flag
• No documented way to persistently enable Chrome for all session types

Related issues: #29486, #40637