MacOS Claude in Chrome — extension never connects; list_connected_browsers and tabs_context_mcp always return "Browser extension is not connected"

The Claude browser MCP tools cannot reach the Chrome extension. Every browser tool call (tabs_context_mcp with createIfEmpty: true, list_connected_browsers) returns the standard "Browser extension is not connected" message. This persisted across ~6 attempts over the session, including after opening a fresh Chrome window at claude.ai and opening the extension popup.

Expected:
list_connected_browsers / tabs_context_mcp should detect the running extension and return at least one connected browser (deviceId, name, platform).

Actual:
Both tools return:

▎ Browser extension is not connected. Please ensure the Claude browser extension is installed and running… you may need to restart Chrome…

list_connected_browsers returning the same "not connected" error (rather than an empty browser list) indicates the pairing/bridge itself never establishes — it's not a browser-selection problem.

Steps to reproduce:

1. Start a Claude Code session with the claude-in-chrome MCP tools available.
2. Ensure the Claude extension is installed and enabled in Chrome, logged into the same claude.ai account.
3. Call tabs_context_mcp (createIfEmpty: true) → "not connected".
4. Open a new Chrome window at claude.ai, open the extension popup, retry list_connected_browsers → still "not connected".

Environment:

• Claude Code powered by model: claude-opus-4-8
• OS: macOS (Darwin 25.5.0), platform darwin
• Chrome version: [fill in — chrome://version]
• Claude extension version: [fill in — chrome://extensions]
• Claude Code version: [fill in — run claude --version]
• claude.ai account in Chrome matches Claude Code account: [fill in — yes/no]
• Full Chrome restart (Cmd+Q) attempted: [fill in — yes/no, and result]
• Additional notes:

Launching Chrome from the shell works fine; only the extension↔Claude-Code MCP bridge fails to connect.