feat(playlists): #417 — "Refreshed …" subtitle on system tiles

Closes the last buildable item of the #411 system-playlists-v2
umbrella. System playlists atomic-replace on rebuild, so created_at
(already on the wire — no server change) is the last-rotated time.
Surface it as a small tile subtitle so users see how fresh a mix
is: "Refreshed just now / today / yesterday / N days ago / Mon D".

- web PlaylistCard: refreshedLabel() + a muted footer line, shown
  only when system_variant != null. Unparseable/empty timestamp →
  suppressed (web test fixtures use created_at:'' so no test churn).
- flutter PlaylistCard: mirrored _refreshedLabel() + subtitle under
  the system badge for isSystem playlists.

Friendly wording deliberately distinct from HistoryRow's "m/h ago";
per-surface helper per the project's existing relative-time
convention. CI-pending; closes with the umbrella on device-check.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

flutter_client/lib/playlists/widgets/playlist_card.dart

@@ -122,6 +122,16 @@ class PlaylistCard extends ConsumerWidget {
                     ),
                   ),
                 ),
+              if (playlist.isSystem && _refreshedLabel(playlist.createdAt) != '')
+                Padding(
+                  padding: const EdgeInsets.only(top: 2),
+                  child: Text(
+                    _refreshedLabel(playlist.createdAt),
+                    maxLines: 1,
+                    overflow: TextOverflow.ellipsis,
+                    style: TextStyle(color: fs.ash, fontSize: 11),
+                  ),
+                ),
             ]),
           ),
         ),
@@ -131,6 +141,27 @@ class PlaylistCard extends ConsumerWidget {
 
   String get _refreshLabel => 'Refresh ${playlist.name}';
 
+  /// #417: system playlists atomic-replace on rebuild, so createdAt
+  /// is the last-rotated time. Friendly wording mirrors the web
+  /// PlaylistCard. Empty string when the timestamp is unparseable.
+  String _refreshedLabel(String iso) {
+    final t = DateTime.tryParse(iso);
+    if (t == null) return '';
+    final now = DateTime.now();
+    final mins = now.difference(t).inMinutes;
+    if (mins < 5) return 'Refreshed just now';
+    final startOfToday = DateTime(now.year, now.month, now.day);
+    if (!t.isBefore(startOfToday)) return 'Refreshed today';
+    final days = startOfToday.difference(DateTime(t.year, t.month, t.day)).inDays;
+    if (days <= 1) return 'Refreshed yesterday';
+    if (days < 7) return 'Refreshed $days days ago';
+    const months = [
+      'Jan', 'Feb', 'Mar', 'Apr', 'May', 'Jun',
+      'Jul', 'Aug', 'Sep', 'Oct', 'Nov', 'Dec',
+    ];
+    return 'Refreshed ${months[t.month - 1]} ${t.day}';
+  }
+
   /// Forces a server-side rebuild of this system playlist, then
   /// invalidates the aggregate list so the rotated UUID + new tracks
   /// land on the next read. ScaffoldMessenger is captured before the

web/src/lib/components/PlaylistCard.svelte

@@ -17,6 +17,27 @@
   // (#411 R2) — no hardcoded kind list here.
   const refreshable = $derived(playlist.refreshable === true);
 
+  // #417: system playlists atomic-replace on rebuild, so created_at
+  // is the last-rotated time. Surface it so users know how fresh the
+  // mix is. Friendly wording, not the HistoryRow "m/h ago" style.
+  function refreshedLabel(iso: string): string {
+    const t = new Date(iso);
+    if (Number.isNaN(t.getTime())) return '';
+    const now = new Date();
+    const mins = Math.floor((now.getTime() - t.getTime()) / 60000);
+    if (mins < 5) return 'Refreshed just now';
+    const startOfToday = new Date(now);
+    startOfToday.setHours(0, 0, 0, 0);
+    const days = Math.floor((startOfToday.getTime() - t.getTime()) / 86400000) + 1;
+    if (t.getTime() >= startOfToday.getTime()) return 'Refreshed today';
+    if (days <= 1) return 'Refreshed yesterday';
+    if (days < 7) return `Refreshed ${days} days ago`;
+    return `Refreshed ${t.toLocaleDateString(undefined, { month: 'short', day: 'numeric' })}`;
+  }
+  const refreshed = $derived(
+    playlist.system_variant != null ? refreshedLabel(playlist.created_at) : ''
+  );
+
   const queryClient = useQueryClient();
 
   let starting = $state(false);
@@ -153,6 +174,9 @@
           · by {playlist.owner_username}
         {/if}
       </div>
+      {#if refreshed}
+        <div class="truncate text-xs text-text-muted">{refreshed}</div>
+      {/if}
     </div>
   </a>
 </div>