Claude in Chrome extension never appears in list_connected_browsers despite correct account, enabled state, and fresh reinstall

The claude-in-chrome MCP tools (tabs_context_mcp, list_connected_browsers) consistently report no connected browser, even after:

• Confirming the extension is logged into the same claude.ai account as Claude Code (verified in the extension's own Settings page, which shows the correct account email)
• Confirming the extension is enabled in chrome://extensions
• Restarting Chrome (full quit, not just closing windows)
• A full remove-and-reinstall of the extension

The extension itself works fine as a standalone side-panel chat (Gmail quick actions like "Unsubscribe from promotional emails," "Archive non-important emails," etc.), and its own Settings > Options / Permissions pages show no visible toggle for pairing with Claude Code.

Observed behavior:

• list_connected_browsers returns [] every time (not even listed as an available-but-unselected option)
• tabs_context_mcp returns: "Browser extension is not connected. Please ensure the Claude browser extension is installed and running (https://claude.ai/chrome), and that you are logged into claude.ai with the same account as Claude Code. If this is your first time connecting to Chrome, you may need to restart Chrome for the installation to take effect."
• switch_browser returns: "No other browsers available to switch to. Open Chrome with the Claude extension in another browser to switch."

Expected behavior: After confirming account match, enabled state, and a fresh install, the extension should appear in list_connected_browsers and/or successfully pair via tabs_context_mcp.

Environment: macOS (Darwin), Claude Code CLI, Chrome with the Claude extension installed from claude.ai/chrome.