Trigger a Sync Automatically When the App Reconnects to the Backend

[TheZupZup]

Overview

Context: SettingsScreen has an auto-sync toggle that runs triggerSync() on a 5-minute Timer. The timer runs continuously regardless of whether the backend is reachable. There is no concept of "just reconnected" — the app doesn't know it was previously disconnected.

This issue adds a simple reconnect-triggered sync: when the app detects the backend has come back online after being unreachable, it triggers a sync immediately (rather than waiting up to 5 minutes for the timer).

What needs to be done

• In AppState, add a _backendReachable boolean (default: true when connected)
• In AppState, add a checkBackendHealth() method that calls ApiClient.ping() → GET /health and updates _backendReachable
• When an API call fails in AppState (any catch block), set _backendReachable = false and notifyListeners()
• In the auto-sync timer callback (SettingsScreen._autoSyncTimer), before triggering sync: if _backendReachable was false, call checkBackendHealth() first — if it passes, set _backendReachable = true and immediately trigger sync
• After a reconnect-triggered sync, also call loadNotebooks() and loadNotes() to refresh the UI with any remote changes

Goal

If the backend was unreachable and then comes back online, the next auto-sync timer tick detects the recovery, syncs immediately, and refreshes the notes list — so the user sees up-to-date content without having to tap "Sync now" manually.

Where to look

• app/lib/services/app_state.dart — add _backendReachable, checkBackendHealth()
• app/lib/screens/settings_screen.dart — _autoSyncTimer callback
• app/lib/services/api_client.dart — ping() method already exists

Edge cases

• The auto-sync toggle is off: no timer runs, so no reconnect-triggered sync either (that's fine — manual sync button still works)
• The backend comes back but WebDAV sync is not configured: trigger loadNotes() refresh but skip triggerSync()

Testing steps

• Enable auto-sync, kill the backend, wait ~5s, restart the backend — verify the app syncs within the next timer tick and notes reload
• Verify _backendReachable transitions correctly from false → true by checking that the snackbar from Surface Sync Results in the Flutter UI (Not Just in the Settings Screen) #17 fires after reconnect

Related to: #17, #22, #24, #26