fix(extension): use offscreen document for persistent WebSocket connection

[lyfuci]

Problem

Chrome MV3 Service Workers are suspended by the browser after a short idle period (~30s). When this happens, the WebSocket connection to the opencli daemon drops silently. Although a keepalive alarm fires every ~24s to wake the SW and call connect(), there is a gap window where:

1. SW is suspended → WS drops
2. Alarm fires → SW wakes → reconnects
3. During that gap, any CLI command gets "Extension not connected"

Users experience this as the extension randomly disconnecting, requiring them to manually click the extension icon to wake it.

Root Cause

The WebSocket connection lives inside the Service Worker. Chrome's MV3 Service Worker lifecycle does not support persistent connections — it is designed to be ephemeral.

Fix

Move the WebSocket connection into a chrome.offscreen document. Offscreen documents have a stable lifetime tied to the browser window (not the SW), so the connection survives SW sleep/wake cycles.

The Service Worker becomes a thin relay layer:

• Receives commands from the daemon CLI
• Forwards them to the offscreen document via chrome.runtime.sendMessage
• Offscreen executes them and sends results back

Changes

File	Change
extension/src/offscreen.ts	✨ New — WebSocket host with auto-reconnect logic
extension/offscreen.html	✨ New — Offscreen document HTML entry point
extension/src/background.ts	🔧 Refactored — SW delegates WS ops to offscreen
extension/manifest.json	🔧 Added offscreen permission
extension/vite.config.ts	🔧 Added offscreen build entry

Testing

Tested on Linux (Chrome 144) with the browser idle for 2+ hours. Extension remained connected throughout — no manual reconnection required.

opencli doctor
[OK] Daemon: running on port 19825
[OK] Extension: connected (v1.5.5)
[OK] Connectivity: connected in 0.2s

Previously this would show [MISSING] Extension: not connected after Chrome suspended the SW.