feat(web/playlists): Discover refresh button (detail + home kebab)

Operator can refresh their Discover playlist without waiting for
the next daily cron tick. Two surfaces, both gated on
system_variant === 'discover':

- Detail page header: "Refresh" button next to the cover art / meta.
- Home Playlists row tile kebab: "Refresh Discover" menu item.

Both call POST /api/playlists/system/discover/refresh, show a
confirmation toast, and invalidate the playlist + playlists queries
so the new content lands without a manual page reload.

Extends Playlist.system_variant union with 'discover'. Adds
refreshDiscover() typed client. Tests cover client behaviour
(success + empty-library) plus conditional rendering on both
surfaces.

web/src/lib/api/playlists.refresh-discover.test.ts

@@ -0,0 +1,31 @@
+import { describe, it, expect, vi, beforeEach } from 'vitest';
+import { refreshDiscover } from './playlists';
+
+vi.mock('./client', () => ({
+  apiFetch: vi.fn()
+}));
+
+import { apiFetch } from './client';
+
+describe('refreshDiscover', () => {
+  beforeEach(() => vi.clearAllMocks());
+
+  it('POSTs the correct path and returns the response', async () => {
+    const sample = { playlist_id: 'abc-123', track_count: 100 };
+    (apiFetch as unknown as ReturnType<typeof vi.fn>).mockResolvedValueOnce(sample);
+    const got = await refreshDiscover();
+    expect(apiFetch).toHaveBeenCalledWith(
+      '/api/playlists/system/discover/refresh',
+      expect.objectContaining({ method: 'POST' })
+    );
+    expect(got).toEqual(sample);
+  });
+
+  it('handles empty-library response', async () => {
+    const sample = { playlist_id: null, track_count: 0 };
+    (apiFetch as unknown as ReturnType<typeof vi.fn>).mockResolvedValueOnce(sample);
+    const got = await refreshDiscover();
+    expect(got.playlist_id).toBe(null);
+    expect(got.track_count).toBe(0);
+  });
+});

web/src/lib/api/playlists.ts

@@ -91,3 +91,20 @@ export function createPlaylistQuery(id: string) {
     staleTime: 30_000
   });
 }
+
+// System playlist refresh ----------------------------------------------------
+
+export type RefreshDiscoverResponse = {
+  playlist_id: string | null;
+  track_count: number;
+};
+
+// Re-runs the daily system playlist build for the calling user and
+// returns the resulting Discover playlist's id + track count.
+// Used by the detail-page Refresh button and the home tile kebab.
+export async function refreshDiscover(): Promise<RefreshDiscoverResponse> {
+  return (await apiFetch('/api/playlists/system/discover/refresh', {
+    method: 'POST',
+    body: JSON.stringify({})
+  })) as RefreshDiscoverResponse;
+}

web/src/lib/api/types.ts

@@ -59,7 +59,7 @@ export type Playlist = {
   description: string;
   is_public: boolean;
   kind: 'user' | 'system';
-  system_variant: 'for_you' | 'songs_like_artist' | null;
+  system_variant: 'for_you' | 'songs_like_artist' | 'discover' | null;
   seed_artist_id: string | null;
   cover_url: string;        // empty string when no cover; UI renders glyph
   track_count: number;