Jellyfin in the app: account linking and library browser

Integrations links several Jellyfin servers (Quick Connect or
password, app-obtained tokens only, status/reconnect/sign out). The
Host tab's Jellyfin source is a full browser: continue watching, next
up, latest per library, library grids with sort/filter/infinite
scroll, series pages with smart resume/next-up, details, grouped
search, inspector pane on wide screens, keyboard navigation.
MediaPicker selection is now a sealed PickedMedia. Hosting a Jellyfin
pick is interim (host's stream URL) until per-viewer playback lands.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

apps/desktop/lib/src/jellyfin/format.dart

@@ -0,0 +1,90 @@
+import 'package:sync_relay_core/core.dart';
+
+import '../screens/home/picked_media.dart';
+import 'accounts.dart';
+
+/// "1 h 42 min", "24 min", "45 s".
+String formatRuntime(Duration d) {
+  final h = d.inHours, m = d.inMinutes % 60;
+  if (h > 0) return m == 0 ? '$h h' : '$h h $m min';
+  if (d.inMinutes > 0) return '${d.inMinutes} min';
+  return '${d.inSeconds} s';
+}
+
+/// Watched share of a resumable item, 0 when there is no resume point.
+double progressOf(JellyfinItem item) {
+  final run = item.runTimeTicks;
+  final pos = item.userData.playbackPositionTicks;
+  if (run == null || run <= 0 || pos <= 0) return 0;
+  return (pos / run).clamp(0.0, 1.0);
+}
+
+/// "12 min left" for a resumable item, else null.
+String? timeLeft(JellyfinItem item) {
+  final run = item.runTimeTicks;
+  if (run == null || !item.userData.isResumable) return null;
+  final left = ticksToDuration(run - item.userData.playbackPositionTicks);
+  if (left.inMinutes < 1) return 'almost done';
+  return '${formatRuntime(left)} left';
+}
+
+bool isPlayable(JellyfinItem item) => switch (item.kind) {
+      JellyfinItemKind.movie || JellyfinItemKind.episode || JellyfinItemKind.video => true,
+      _ => !item.isFolder && item.mediaType == 'Video',
+    };
+
+/// Line under a card title: "S2E3 · 12 min left", "2019 · 24 eps", ...
+String cardSubtitle(JellyfinItem item, {bool withSeries = false}) {
+  final parts = <String>[];
+  switch (item.kind) {
+    case JellyfinItemKind.episode:
+      if (withSeries && item.seriesName != null) parts.add(item.seriesName!);
+      parts.add(item.episodeLabel ?? item.seasonName ?? 'Episode');
+    case JellyfinItemKind.series:
+      if (item.productionYear != null) parts.add('${item.productionYear}');
+      final eps = item.recursiveItemCount, seasons = item.childCount;
+      if (eps != null && eps > 0) {
+        parts.add('$eps eps');
+      } else if (seasons != null && seasons > 0) {
+        parts.add(seasons == 1 ? '1 season' : '$seasons seasons');
+      }
+    case JellyfinItemKind.season:
+      final n = item.childCount ?? item.recursiveItemCount;
+      if (n != null) parts.add('$n eps');
+    default:
+      if (item.productionYear != null) parts.add('${item.productionYear}');
+  }
+  final left = timeLeft(item);
+  if (left != null) {
+    parts.add(left);
+  } else if (isPlayable(item) && item.runTime != null) {
+    parts.add(formatRuntime(item.runTime!));
+  }
+  return parts.join(' · ');
+}
+
+/// Title on a card: episodes in rows that mix series show the series name
+/// on top and the episode below.
+String cardTitle(JellyfinItem item, {bool seriesFirst = false}) =>
+    seriesFirst && item.kind == JellyfinItemKind.episode && item.seriesName != null
+        ? item.seriesName!
+        : item.name;
+
+/// The selection for a playable [item] of [account].
+JellyfinMedia pickFor(JellyfinAccount account, JellyfinItem item) {
+  final String subtitle;
+  if (item.kind == JellyfinItemKind.episode) {
+    subtitle = [?item.seriesName, ?item.episodeLabel].join(' · ');
+  } else {
+    subtitle = item.productionYear?.toString() ?? '';
+  }
+  return JellyfinMedia(
+    serverId: account.serverId,
+    baseUrl: account.baseUrl,
+    itemId: item.id,
+    mediaSourceId: item.mediaSources.length > 1 ? item.mediaSources.first.id : null,
+    title: item.name,
+    subtitle: subtitle,
+    runtime: item.runTime,
+  );
+}