Add device sync: mirror folders/files locally, background WorkManager engine

- New native sync engine (SyncEngine/SyncWorker/ConflictResolveWorker,
  WorkManager-based) that mirrors selected Nextcloud folders or files to
  app-private local storage, periodically and on-demand ("Sync now"),
  with never-auto-resolved conflict notifications.
- Single files (not just folders) can now be marked "Sync to device".
- Live sync status (syncing/synced/conflicts) pushes from native to Dart
  over a new EventChannel; the persistent header chip/panel now reflects
  device-sync status instead of the WebDAV-refresh loading state, with a
  cloud_off/cloud_sync/cloud_done/cloud_alert icon set and an expandable
  conflicts list with in-app "Keep local"/"Use server" resolution.
  Per-item cloud_done/sync badges show on Files tiles.
- Share/Download short-circuit to the local copy for already-synced
  files instead of a fresh network fetch.
- Settings gained a Device Sync section (per-folder list, "Sync
  everything", Wi-Fi-only toggle, manual "Sync now").
- Fixed two release-only bugs found via on-device testing: Android's
  HttpURLConnection silently rejects the PROPFIND method (switched to
  OkHttp), and R8 was stripping WorkManager's reflection-instantiated
  internals (broadened proguard-rules.pro to keep androidx.work.**
  wholesale rather than chasing individual classes).

Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>

.claude/context/styling.md

@@ -63,7 +63,17 @@ widgets. Key points:
 - [`SyncedHeaderScaffold`](../../lib/widgets/synced_header_scaffold.dart) —
   the pull-to-sync `CustomScrollView` header shared by 5 of the 6 tabs (see
   `architecture.md`); also where the pull-to-refresh gesture thresholds and
-  the classic Material refresh spinner live.
+  the classic Material refresh spinner live. Its persistent chip/panel
+  (icon + "Sync off"/"Syncing…"/"Synced"/"Sync issue") reflects device-sync
+  status (`ServerProvider.syncHeaderStatus`), not the WebDAV-refresh
+  loading state the pull gesture itself triggers - that has its own,
+  separate floating spinner bubble, so nothing was lost by handing the
+  persistent text/icon over.
+- [`SyncStatusBadge`](../../lib/widgets/sync_status_badge.dart) — the small
+  corner badge over a thumbnail showing per-item device-sync status
+  (`cloud_done`/`sync`, nothing for not-synced/conflict); used in Files'
+  list and grid tiles today. Reuse this rather than a new ad hoc badge if
+  another view starts showing sync status per item.
 - [`SeekBarPainter`/`SeekBarPreview`](../../lib/widgets/seek_bar_painter.dart)
   — the four `MediaProgressBarStyle` presets (Default/Wavy/Slim/Squiggly)
   for the video player's seek bar, plus a perpetually-animated