feat(web/m7-scan-progress): StageBadge + 4-card layout updates

Each of the 4 stage cards in the admin Library Scan section gains a
StageBadge in its header. The badge derives state via stageState()
from the existing ScanStatus payload — no new query, no schema
change. Active stage shows spinner + "Processing" in moss green;
done shows check + "Done" in moss green; pending and skipped show
muted text.

Card body now shows either the (possibly partial) numbers OR a
"Waiting for previous stage…" placeholder when the badge is
pending. The previous bottom-of-card "Pending…" / "Skipped."
fallback text disappears (the badge replaces it).

StageBadge.test.ts covers the four state renderings.
admin.test.ts adds one new case asserting the Processing badge
shows when scan.library is populated and in_flight: true. Existing
admin.test.ts assertions still pass (the default mock data has no
stage tallies + in_flight: false → all stages skipped, no Loader/
Check icons rendered).

web/src/routes/admin/admin.test.ts

@@ -22,12 +22,13 @@ vi.mock('$lib/api/admin', async () => {
     createAdminRequestsQuery: vi.fn(),
     createLidarrConfigQuery: vi.fn(),
     createAdminQuarantineQuery: vi.fn(),
-    createScanStatusQuery: () =>
+    createScanStatusQuery: vi.fn(() =>
       readable({
         data: { id: '', started_at: '', finished_at: null, in_flight: false },
         isPending: false,
         isError: false
-      }),
+      })
+    ),
     createCoverageQuery: () =>
       readable({
         data: undefined,
@@ -91,6 +92,7 @@ import {
   createAdminRequestsQuery,
   createLidarrConfigQuery,
   createAdminQuarantineQuery,
+  createScanStatusQuery,
   approveRequest,
   rejectRequest,
   resolveQuarantine,
@@ -239,4 +241,25 @@ describe('admin Overview page', () => {
       'href', '/admin/requests'
     );
   });
+
+  test('Library scan card shows Processing badge when library tally is populated and in-flight', async () => {
+    const { readable } = await import('svelte/store');
+    (createScanStatusQuery as ReturnType<typeof vi.fn>).mockReturnValueOnce(
+      readable({
+        data: {
+          id: 'in-flight',
+          started_at: '2026-05-06T11:00:00Z',
+          finished_at: null,
+          in_flight: true,
+          library: { scanned: 100, added: 1, updated: 0, skipped: 99, errored: 0 }
+        },
+        isPending: false,
+        isError: false
+      })
+    );
+    setupOverview();
+    userState.current = { id: 'admin', username: 'admin', is_admin: true };
+    render(OverviewPage);
+    expect(await screen.findByText('Processing')).toBeInTheDocument();
+  });
 });