feat(translation): live re-translate progress in the Settings card

translation/status now reports `active` (a translate/retranslate sweep is
running, from the TaskRun table) and `last_run` (the most recent finished run's
task + status). The Settings card polls live while a sweep runs, showing a
spinner + "Translating… N remaining" that ticks down, and flags a last run that
ended in error/timeout. No migration.

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

tests/test_api_settings.py

@@ -61,6 +61,34 @@ async def test_translation_status_defaults(client):
     assert body["base_url_set"] is False
     assert body["healthy"] is False
     assert "untranslated_count" in body
+    assert body["active"] is False      # no sweep running
+    assert body["last_run"] is None
+
+
+@pytest.mark.asyncio
+async def test_translation_status_reports_active_and_last_run(client, db):
+    # A running translate/retranslate TaskRun → active True; the most recent
+    # finished one → last_run (task basename + status).
+    from datetime import UTC, datetime
+
+    from backend.app.models import TaskRun
+
+    db.add(TaskRun(
+        celery_task_id="r-run", queue="maintenance_long",
+        task_name="backend.app.tasks.translation.retranslate_posts",
+        started_at=datetime.now(UTC), status="running",
+    ))
+    db.add(TaskRun(
+        celery_task_id="r-done", queue="maintenance_long",
+        task_name="backend.app.tasks.translation.translate_posts",
+        started_at=datetime.now(UTC), finished_at=datetime.now(UTC),
+        status="success",
+    ))
+    await db.commit()
+    body = await (await client.get("/api/settings/translation/status")).get_json()
+    assert body["active"] is True
+    assert body["last_run"]["task"] == "translate_posts"
+    assert body["last_run"]["status"] == "success"
 
 
 @pytest.mark.asyncio