feat(web/playlists): For-You tile play button refreshes and plays

Click on the For-You tile's play button now triggers a synchronous
refresh, then enqueues + auto-plays the freshly-built playlist.
Two-click-target tile pattern: tile BODY click still navigates to
the playlist detail page (existing behavior); the play button is
the new generate-and-play action.

Behavior is gated on playlist.system_variant === 'for_you' — every
other playlist (user, Discover, Songs-like-X) keeps the existing
"fetch detail, enqueue, play" flow. The atomic-replace BuildSystem-
Playlists creates a new playlist_id, so the play handler uses the
refresh response's id for the follow-up getPlaylist call rather
than the stale tile prop's id.

Empty-library response (playlist_id: null) is a no-op — clicking
play in a degenerate-empty library doesn't error, it just doesn't
start playback. Caches are invalidated post-refresh so the home
view re-fetches and the tile re-renders with the new id, avoiding
the corner case of a click-then-tile-body 404.

Tests cover the refresh-and-play happy path, the empty-library
no-op, and that non-For-You playlists keep the existing flow.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

web/src/lib/api/playlists.ts

@@ -108,3 +108,24 @@ export async function refreshDiscover(): Promise<RefreshDiscoverResponse> {
     body: JSON.stringify({})
   })) as RefreshDiscoverResponse;
 }
+
+// For-You refresh ------------------------------------------------------------
+
+export type RefreshForYouResponse = {
+  playlist_id: string | null;
+  track_count: number;
+  track_ids: string[];
+};
+
+// POST /api/playlists/system/for-you/refresh — synchronously
+// rebuilds the calling user's For-You playlist and returns the new
+// id, track count, and track id list.
+//
+// Used by the home Playlists row's For-You tile play button: click
+// triggers refresh, the frontend then calls getPlaylist(new_id) to
+// get full TrackRef snapshots and enqueues for playback.
+export async function refreshForYou(): Promise<RefreshForYouResponse> {
+  return (await apiFetch('/api/playlists/system/for-you/refresh', {
+    method: 'POST'
+  })) as RefreshForYouResponse;
+}