feat(admin): show the newest database dump on the backups page

GET /api/admin/backups now carries `database`: the newest good dump (when,
how big, kept on the server, off-host or both), the newest failed run,
whether this server can write its backup directory, and whether off-host
copies are configured. The backups card leads with one row built from it,
with a notice when the last run failed and when dumps can only go
off-host or cannot be taken at all. The route stays an unpublished admin
console route, so the OpenAPI document does not change.

src/components/admin/backups-section.tsx

@@ -28,6 +28,7 @@ import type { BackupRow, BackupsList } from "@/types/backups";
 
 import { RestoreJobStatus, visibleRestoreJobs } from "./backup-restore-status";
 import { BackupRowsCards, BackupRowsTable } from "./backups/backup-rows";
+import { DatabaseDumpRow } from "./backups/database-dump-row";
 import { BackupUploadCard } from "./backups/backup-upload-card";
 import {
   RestoreRefusalNotice,
@@ -110,6 +111,7 @@ export function BackupsSection() {
         }
       />
 
+      {data?.database ? <DatabaseDumpRow health={data.database} /> : null}
       {data?.schedule ? (
         <ScheduleHealthNotice schedule={data.schedule} />
       ) : null}