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/player/events.svelte.ts

@@ -92,7 +92,11 @@ export function useEventsDispatcher(): void {
       const res = await api.post<PlayStartedResponse>('/api/events', {
         type: 'play_started',
         track_id: trackId,
-        client_id: clientId
+        client_id: clientId,
+        // #415: tag the play with the system playlist it came from
+        // (null for library / user-playlist / radio) so the server
+        // can advance that playlist's rotation.
+        source: player.queueSource ?? undefined
       });
       // The user may have moved on by the time the response arrives. Only
       // adopt the id if we're still on the same track and still playing.

web/src/lib/player/store.svelte.ts

@@ -41,6 +41,13 @@ let _pendingRestorePosition: number | null = null;
 let _radioSeedId          = $state<string | null>(null);
 let _radioRefreshInFlight = false;
 
+// #415: which system playlist (if any) this queue was seeded from.
+// 'for_you' | 'discover' | null. Read by the events dispatcher so
+// play_started carries `source` and the play counts against that
+// playlist's rotation. Re-set on every playQueue (a fresh non-system
+// queue clears it).
+let _queueSource = $state<string | null>(null);
+
 let _audioEl: HTMLAudioElement | null = null;
 
 export const player = {
@@ -55,6 +62,7 @@ export const player = {
   get shuffle()   { return _shuffle; },
   get repeat()    { return _repeat; },
   get error()     { return _error; },
+  get queueSource()       { return _queueSource; },
   get queueDrawerOpen()   { return _queueDrawerOpen; }
 };
 
@@ -65,9 +73,13 @@ export function registerAudioEl(el: HTMLAudioElement | null): void {
 export function playQueue(
   tracks: TrackRef[],
   startIndex = 0,
-  opts: { shuffle?: boolean } = {},
+  opts: { shuffle?: boolean; source?: string | null } = {},
 ): void {
   _radioSeedId = null;  // M4c: non-radio enqueue clears the radio refresh state
+  // #415: a fresh queue resets the system-playlist source. Set only
+  // when seeded from a system playlist (server already returned the
+  // rotation-aware order, so no client shuffle in that path).
+  _queueSource = opts.source ?? null;
   if (opts.shuffle && tracks.length > 1) {
     // Fisher-Yates over the whole list. startIndex is ignored — the
     // caller is asking for "random play from this pool," so the first