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 The route stays an unpublished admin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}

src/components/admin/backups/database-dump-row.tsx

@@ -0,0 +1,114 @@
+"use client";
+
+/**
+ * The nightly whole-database dump, as one row on the backups card.
+ *
+ * The account copies below it restore one account on this server; the dump is
+ * the copy that rebuilds the server. So the row leads the card and says three
+ * things: when the newest good dump was taken and where it is, whether the
+ * newest run failed, and whether this server can keep a dump at all.
+ */
+import { AlertTriangle, HardDrive } from "lucide-react";
+
+import { SettingsInfoTile } from "@/components/settings/_info-tile";
+import { formatBytes } from "@/lib/format/bytes";
+import { useFormatters, useTranslations } from "@/lib/i18n/context";
+import type { DatabaseBackupHealth } from "@/lib/database-backup/health";
+
+function whereKept(
+  good: NonNullable<DatabaseBackupHealth["lastGood"]>,
+  t: ReturnType<typeof useTranslations>["t"],
+) {
+  if (good.local && good.offhost) {
+    return t("admin.section.backups.database.whereBoth");
+  }
+  if (good.offhost) return t("admin.section.backups.database.whereOffhost");
+  return t("admin.section.backups.database.whereLocal");
+}
+
+export function DatabaseDumpRow({ health }: { health: DatabaseBackupHealth }) {
+  const { t, locale } = useTranslations();
+  const fmt = useFormatters();
+  const good = health.lastGood;
+  const failure = health.lastFailure;
+  const failedSinceGood =
+    failure !== null && (good === null || failure.at > good.at);
+
+  let setupProblem: string | null = null;
+  if (!health.enabled) {
+    setupProblem = t("admin.section.backups.database.disabled");
+  } else if (!health.localDirWritable) {
+    setupProblem = health.offhostConfigured
+      ? t("admin.section.backups.database.noDirectoryOffhost", {
+          dir: health.directory,
+        })
+      : t("admin.section.backups.database.noDirectory", {
+          dir: health.directory,
+        });
+  }
+
+  return (
+    <div className="space-y-2" data-slot="database-dump">
+      <div className="flex items-start gap-2">
+        <HardDrive
+          className="text-muted-foreground mt-0.5 h-4 w-4 shrink-0"
+          aria-hidden="true"
+        />
+        <div>
+          <p className="text-sm font-medium">
+            {t("admin.section.backups.database.title")}
+          </p>
+          <p
+            className="text-muted-foreground text-xs"
+            data-slot="database-dump-last-good"
+          >
+            {good
+              ? t("admin.section.backups.database.lastGood", {
+                  when: fmt.dateTime(good.at),
+                  size: formatBytes(good.sizeBytes ?? 0, locale),
+                  where: whereKept(good, t),
+                })
+              : t("admin.section.backups.database.none")}
+          </p>
+        </div>
+      </div>
+
+      {failedSinceGood && failure ? (
+        <div
+          role="alert"
+          data-slot="database-dump-failed"
+          className="border-destructive/40 bg-destructive/10 rounded-md border px-3 py-2 text-sm"
+        >
+          <div className="flex items-start gap-2">
+            <AlertTriangle
+              className="mt-0.5 h-4 w-4 shrink-0"
+              aria-hidden="true"
+            />
+            <div>
+              <p className="font-medium">
+                {t("admin.section.backups.database.failedTitle")}
+              </p>
+              <p className="text-xs">
+                {t("admin.section.backups.database.failedDescription", {
+                  when: fmt.dateTime(failure.at),
+                  reason: failure.error,
+                })}
+              </p>
+            </div>
+          </div>
+        </div>
+      ) : null}
+
+      {setupProblem ? (
+        <SettingsInfoTile
+          icon={AlertTriangle}
+          tone="warning"
+          role="alert"
+          data-slot="database-dump-setup"
+        >
+          {setupProblem}
+        </SettingsInfoTile>
+      ) : null}
+    </div>
+  );
+}