GitHub asset name includes a v prefix (v0.8.0) while
CFBundleShortVersionString does not (0.8.0). Strip the prefix
before comparing. Also capture stderr on update failure so the
button doesn't hang on "Updating..." forever.
Remove the broken "Connect Claude" / "Reconnect Claude" buttons from
the Plan pane -- they opened a terminal session that did nothing useful
for already-logged-in users. Keep only the "Retry" button.
Add an auto-update checker that queries GitHub releases every 2 days in
the background. When a newer menubar build is available, an "Update"
pill appears in the header. Clicking it runs the existing installer
flow (download, replace, relaunch) with no manual steps.