Claude in Chrome extension never pairs with cloud Cowork session (all documented conditions met)

Environment

• macOS (Apple Silicon), Claude desktop app 1.26832.0 (Electron 42.7.0)
• Chrome current stable; extension freshly installed from claude.ai/chrome (store shows "Remove from Chrome")
• Active paid Claude plan; session type: cloud Cowork task connected to this desktop via device bridge

Bug
Every tabs_context_mcp call (with and without createIfEmpty) returns "Browser extension is not connected", across several hours and retries.

All documented troubleshooting completed and re-verified

1. Extension installed and current (installed same day)
2. Chrome fully quit and relaunched, multiple times
3. Signed into claude.ai in Chrome with the same account as the session
4. Extension granted full site access
5. Desktop app's Claude in Chrome Connector toggle already enabled
6. Paid plan active (cloud Cowork sessions running)
7. claude-in-chrome skill invoked before tool calls — same result

Notes

• Same device pairs Chrome read-only screenshots fine via computer-use, so the device bridge is healthy.
• Impact: solo artist blocked on browser automation for store setup (login-gated SaaS UIs); extension is the documented path and never pairs.

Ask
Is extension pairing supported for cloud Cowork sessions? If yes, what else can be checked (multiple Chrome profiles? native messaging host registration?). If no, please document the limitation.