feat(web): #415 stage 3 (web) — rotation-aware system playlist play

Web half of Stage 3. System-playlist tile play now:
- calls the new GET /api/playlists/system/{variant}/shuffle endpoint
  (rotation-aware order from the server) instead of getPlaylist;
  plays the returned order AS-IS — no client Fisher-Yates, since
  the server already ordered it. Supersedes #413's client shuffle
  for system playlists specifically; user playlists keep getPlaylist
  + stored order.
- tags the queue with the system variant. The player store carries
  _queueSource; the events dispatcher includes `source` on
  play_started so the server advances that playlist's rotation.

User playlists are unchanged (getPlaylist, plain playQueue, no
source). Tests updated: For-You play hits systemShuffle (not
getPlaylist/refresh) and passes source:for_you; user play uses
getPlaylist + plain playQueue with no source.

Flutter half is blocked — the Flutter client has no play-event
reporting at all (no /api/events POST, no scrobble), so there's no
play_started to attach `source` to. Surfacing that as a separate
decision rather than silently scope-exploding #415.

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

web/src/lib/components/PlaylistCard.svelte

@@ -3,7 +3,7 @@
   import { useQueryClient } from '@tanstack/svelte-query';
   import type { Playlist, PlaylistTrack, TrackRef } from '$lib/api/types';
   import { user } from '$lib/auth/store.svelte';
-  import { getPlaylist, refreshDiscover, refreshForYou } from '$lib/api/playlists';
+  import { getPlaylist, systemShuffle, refreshDiscover, refreshForYou } from '$lib/api/playlists';
   import { playlistTrackToRef } from '$lib/playlists/playlistTrackToRef';
   import { errCode } from '$lib/api/errors';
   import { qk } from '$lib/api/queries';
@@ -45,14 +45,23 @@
     if (starting) return;
     starting = true;
     try {
-      const detail = await getPlaylist(playlist.id);
-      const refs = toTrackRefs(detail.tracks);
-      if (refs.length > 0) {
-        // System playlists default to shuffle so replaying within a
-        // day feels different. User playlists keep stored order.
-        // Explicit refresh moved to the kebab menu — playing no
-        // longer rebuilds the snapshot.
-        playQueue(refs, 0, { shuffle: playlist.system_variant != null });
+      const variant = playlist.system_variant;
+      if (variant != null) {
+        // #415: server returns the rotation-aware order (unplayed
+        // this rotation first). Play it as-is — no client shuffle —
+        // and tag the queue so play_started carries `source` and
+        // the server advances the rotation.
+        const detail = await systemShuffle(variant);
+        const refs = toTrackRefs(detail.tracks);
+        if (refs.length > 0) {
+          playQueue(refs, 0, { source: variant });
+        }
+      } else {
+        const detail = await getPlaylist(playlist.id);
+        const refs = toTrackRefs(detail.tracks);
+        if (refs.length > 0) {
+          playQueue(refs, 0);
+        }
       }
     } finally {
       starting = false;