feat(analysis): live SSE updates in the admin coverage dashboard

The Analysis section now reflects worker progress in real time:

- Opens an EventSource on the live stream while mounted; a "Live" pill
  reflects connection state and reconnects on drop (probes after repeated
  failures so a lost session logs out).
- Applies events incrementally: enqueued marks in-scope loaded pages
  queued; started flips a chip to a pulsing "analyzing"; completed flips
  it green and live-bumps the manga + chapter coverage badges (guarded so
  no double count); failed flips it red. A compact activity ticker shows
  the last few events.
- Server numbers stay authoritative: re-loading the overview or a page
  grid clears the matching live overrides.

API client: analysisStatusStreamUrl() + AnalysisEvent type.

Tests: vitest for the stream URL; Playwright asserts SSE frames flow into
the ticker (existing coverage/drill/queue specs get a default quiet
stream). svelte-check + build clean.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

frontend/e2e/admin-analysis.spec.ts

@@ -155,6 +155,14 @@ async function mockAdmin(page: Page, cap: Captured) {
         })
     );
 
+    // Default: keep the SSE connection pending (no events) so tests that
+    // don't care about live updates don't trigger reconnect churn. The
+    // live-updates test overrides this with a fulfilling stream.
+    await page.route(
+        '**/api/v1/admin/analysis/status/stream',
+        () => new Promise(() => {})
+    );
+
     await page.route('**/api/v1/admin/analysis/reenqueue', (r) => {
         cap.reenqueue = JSON.parse(r.request().postData() ?? '{}');
         return r.fulfill({
@@ -221,6 +229,49 @@ test.describe('/admin/analysis', () => {
         );
     });
 
+    test('live SSE events drive the indicator and activity ticker', async ({
+        page
+    }) => {
+        const cap: Captured = { reenqueue: null, analyzeCalls: 0 };
+        await mockAdmin(page, cap);
+        // Override the default hanging stream with one that emits two frames.
+        const frames =
+            `event: analysis\ndata: ${JSON.stringify({
+                kind: 'started',
+                page_id: pageNone,
+                manga_id: mangaId,
+                chapter_id: chapterId,
+                page_number: 2
+            })}\n\n` +
+            `event: analysis\ndata: ${JSON.stringify({
+                kind: 'completed',
+                page_id: pageNone,
+                manga_id: mangaId,
+                chapter_id: chapterId,
+                page_number: 2
+            })}\n\n`;
+        let served = false;
+        await page.route('**/api/v1/admin/analysis/status/stream', (r) => {
+            if (served) return new Promise(() => {}); // hang on reconnect
+            served = true;
+            return r.fulfill({
+                status: 200,
+                headers: { 'content-type': 'text/event-stream' },
+                body: frames
+            });
+        });
+
+        await page.setViewportSize(DESKTOP);
+        await page.goto('/admin/analysis');
+
+        // The two SSE frames are parsed and applied to the activity ticker.
+        // (The mocked stream closes after its body, so the live pill flips
+        // back to "Reconnecting…" — the ticker is the durable signal.)
+        const tick = page.getByTestId('admin-analysis-ticker');
+        await expect(tick).toContainText('Analyzing page 2');
+        await expect(tick).toContainText('Analyzed page 2');
+    });
+
     test('queue an unanalyzed page from its detail modal', async ({ page }) => {
         const cap: Captured = { reenqueue: null, analyzeCalls: 0 };
         await mockAdmin(page, cap);