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>

backend/app/api/settings.py

@@ -16,6 +16,7 @@ from ..models import (
     ImportTask,
     Post,
     Tag,
+    TaskRun,
 )
 from ..services import interpreter_client as ic
 
@@ -306,6 +307,10 @@ async def translation_status():
     """For the Settings card: is it on, is a URL set, is the service reachable,
     and how many posts still await translation. Health runs the sync client in a
     thread so the event loop isn't blocked."""
+    translation_tasks = (
+        "backend.app.tasks.translation.translate_posts",
+        "backend.app.tasks.translation.retranslate_posts",
+    )
     async with get_session() as session:
         cfg = await ImportSettings.load(session)
         untranslated = (await session.execute(
@@ -315,6 +320,21 @@ async def translation_status():
                 Post.post_title.is_not(None), Post.description.is_not(None),
             ))
         )).scalar_one()
+        # Live progress: is a sweep running now, and what did the last one do?
+        # (run-until-done re-enqueues itself, so `active` stays true across a
+        # bulk re-translate; `last_run` surfaces a completed run's outcome.)
+        active = (await session.execute(
+            select(func.count(TaskRun.id))
+            .where(TaskRun.task_name.in_(translation_tasks))
+            .where(TaskRun.status == "running")
+        )).scalar_one()
+        last = (await session.execute(
+            select(TaskRun.task_name, TaskRun.status, TaskRun.finished_at)
+            .where(TaskRun.task_name.in_(translation_tasks))
+            .where(TaskRun.finished_at.is_not(None))
+            .order_by(TaskRun.finished_at.desc())
+            .limit(1)
+        )).first()
     base_url = (cfg.interpreter_base_url or "").strip()
     healthy = await asyncio.to_thread(ic.health, base_url) if base_url else False
     return jsonify({
@@ -322,6 +342,12 @@ async def translation_status():
         "base_url_set": bool(base_url),
         "healthy": healthy,
         "untranslated_count": int(untranslated),
+        "active": int(active) > 0,
+        "last_run": {
+            "task": last[0].rsplit(".", 1)[-1],
+            "status": last[1],
+            "finished_at": last[2].isoformat() if last[2] else None,
+        } if last else None,
     })