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/api/playlists.ts

@@ -19,6 +19,18 @@ export async function getPlaylist(id: string): Promise<PlaylistDetail> {
   return api.get<PlaylistDetail>(`/api/playlists/${encodeURIComponent(id)}`);
 }
 
+// #415 stage 2/3: rotation-aware play order for a system playlist.
+// Same shape as getPlaylist but tracks are server-ordered (unplayed
+// this rotation first, then heard; resets when exhausted). The model
+// variant uses underscores; the route segment is hyphenated.
+// Intentionally uncached — it varies per play, unlike getPlaylist.
+export async function systemShuffle(variant: string): Promise<PlaylistDetail> {
+  const seg = variant === 'for_you' ? 'for-you' : variant;
+  return api.get<PlaylistDetail>(
+    `/api/playlists/system/${encodeURIComponent(seg)}/shuffle`,
+  );
+}
+
 export type CreatePlaylistInput = {
   name: string;
   description?: string;