Mirrors the rail's unread-chat count onto the Windows taskbar icon (overlay) and the
macOS/Linux dock badge. updateRailUnread() draws a small red count badge on a canvas
and hands it to the shell via bizConnectNative.setUnread(count, dataUrl); main sets it
with win.setOverlayIcon + app.setBadgeCount. Clears at 0, shows 99+ past 99. No-op in a
browser/mobile. (home.html build batch17)
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>