Answer
Do PWAs support background sync?
Partially. Chromium browsers (Chrome, Edge, Android WebView, Samsung Internet) support the Background Sync API for retrying failed requests, and Periodic Background Sync for scheduled updates. iOS Safari and Firefox do not support either. Fall back to Push notifications for cross-platform re-engagement.
One-shot Background Sync
Register a sync tag when a request fails. The browser retries it once connectivity returns, even if the tab is closed. Widely supported on Chromium.
Periodic Background Sync
Runs a task at roughly daily intervals. Chrome only, requires a "high site engagement" score, and users can disable it in browser settings.
The iOS workaround
iOS Safari does not implement either API. Use silent Web Push (via Notification.showNotification with silent: false is required) to wake the SW and refresh caches.