feat: the Backups screen says whether backups are keeping up, and the System view warns when they aren't

- A Backups row on Settings → System and the nav dot turn amber when the
  newest database dump is more than a day old or failed, or the weekly
  bucket check found files missing that no media run has sent since.
  No row when backups aren't set up.
- The weekly bucket check is kept as a run (kind "reconcile") with its
  counts, trimmed to the last 12, and listed on the Backups card.
- The Backups card leads with the same verdict and the newest dump's size,
  shows bytes beside the running media job's file count, and lets each run
  open its list of failed files with why.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

backend/app/api/system_backup.py

@@ -20,7 +20,7 @@ system_backup_bp = Blueprint(
     "system_backup", __name__, url_prefix="/api/system/backup",
 )
 
-_KINDS = frozenset({"db", "images", "media", "restore"})
+_KINDS = frozenset({"db", "images", "media", "restore", "reconcile"})
 _TAG_MAX_LEN = 64
 _BACKUP_SETTINGS_FIELDS = (
     "backup_db_nightly_enabled",

backend/app/api/system_health.py

@@ -35,6 +35,7 @@ from sqlalchemy import select, text
 from ..config import get_config
 from ..extensions import get_session
 from ..models import ServiceSeen
+from ..services import backup_health
 from ..services.worker_lanes import SWEEP_PERIOD_SECONDS
 
 system_health_bp = Blueprint("system_health", __name__, url_prefix="/api/system")
@@ -227,6 +228,17 @@ async def system_health():
                     **{k: v for k, v in (row.details or {}).items() if k != "agent_id"},
                 })
 
+            # Whether the backups are keeping up. Read like the rest, and a
+            # failure to read it is reported as unknown rather than raised.
+            try:
+                backup = await session.run_sync(lambda s: backup_health.backup_part(s, now))
+            except Exception as exc:  # noqa: BLE001 — a probe reports, it never raises
+                backup = {"key": "backup", "kind": "backup", "name": "Backups",
+                          "state": _UNKNOWN,
+                          "detail": f"could not be checked: {type(exc).__name__}"}
+            if backup is not None:
+                parts.append(backup)
+
     parts.append(await _probe_redis())
 
     overall = max((p["state"] for p in parts), key=lambda s: _SEVERITY[s], default=_UNKNOWN)