fix(exam): reflect authoritative exam state and lock engine-graded results

- COC queue status cell shows the server-derived exam state (registered,
  present, sat, passed, failed) instead of the lagging application status.
- Portal examStageFor prefers the server's examState so portal and back
  office never disagree; NOT_SITTING stage added.
- Exam roster shows each candidate's result and lock; Regrade hidden once
  a result exists.
- Record Result modal: only unmarked candidates, empty score boxes (no
  silent zeros), reason required, backend refusals translated.
- Result page: auto-graded marks read-only, per-applicant publish.
- Exam page: session window fields, Add Question menu (bank / Excel /
  scratch), wait metrics panel; PUBLISHED exam status removed.
- Portal: exam window shown, early launch and eligibility refusals explained.

Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>

apps/backoffice/src/app/features/exam/components/ExamWaitMetricsPanel.tsx

@@ -0,0 +1,67 @@
+import { useTranslation } from 'react-i18next';
+import { Group, Paper, SimpleGrid, Text, Title, Badge } from '@mantine/core';
+import { IconHourglass } from '@tabler/icons-react';
+import { useGetExamWaitMetricsQuery } from '../api/exam-api';
+import type { WaitStat } from '../types/exam';
+
+function minutes(value: number | null, t: (key: string, options?: Record<string, unknown>) => string): string {
+  if (value === null) return '—';
+  const abs = Math.abs(value);
+  const label =
+    abs >= 1440
+      ? t('exam.metrics.days', { value: Math.round((abs / 1440) * 10) / 10 })
+      : abs >= 60
+        ? t('exam.metrics.hours', { value: Math.round((abs / 60) * 10) / 10 })
+        : t('exam.metrics.minutes', { value: Math.round(abs * 10) / 10 });
+  return value < 0 ? `−${label}` : label;
+}
+
+function StatCard({ label, stat, t }: { label: string; stat: WaitStat; t: (key: string, options?: Record<string, unknown>) => string }) {
+  return (
+    <Paper withBorder radius="md" p="md">
+      <Text fz="xs" c="dimmed" tt="uppercase" fw={600}>{label}</Text>
+      <Text fz={22} fw={700} mt={4}>{minutes(stat.averageMinutes, t)}</Text>
+      <Text fz="xs" c="dimmed">{t('exam.metrics.average')}</Text>
+      <Group gap="md" mt="xs">
+        <Text fz="xs">{t('exam.metrics.min')}: <b>{minutes(stat.minMinutes, t)}</b></Text>
+        <Text fz="xs">{t('exam.metrics.max')}: <b>{minutes(stat.maxMinutes, t)}</b></Text>
+        <Text fz="xs">{t('exam.metrics.count')}: <b>{stat.count}</b></Text>
+      </Group>
+    </Paper>
+  );
+}
+
+/**
+ * Exam wait metrics — how long candidates waited at each step up to the
+ * sitting, read off the registration, attendance and attempt timestamps
+ * the workflow already writes. Analytics only: nothing here can change a
+ * registration, an attendance ruling, a result or a certificate.
+ */
+export function ExamWaitMetricsPanel({ examId }: { examId: string }) {
+  const { t } = useTranslation();
+  const { data, isError } = useGetExamWaitMetricsQuery(examId);
+  if (isError || !data) return null;
+
+  return (
+    <Paper withBorder radius="lg" p="lg">
+      <Group justify="space-between" mb="xs">
+        <Group gap="xs">
+          <IconHourglass size={18} />
+          <Title order={5}>{t('exam.metrics.section')}</Title>
+        </Group>
+        <Group gap="xs">
+          <Badge variant="light" color="gray">{t('exam.metrics.candidates', { count: data.candidateCount })}</Badge>
+          <Badge variant="light" color="teal">{t('exam.metrics.attended', { count: data.attendedCount })}</Badge>
+          <Badge variant="light" color="blue">{t('exam.metrics.started', { count: data.startedCount })}</Badge>
+        </Group>
+      </Group>
+      <Text fz="xs" c="dimmed" mb="md">{t('exam.metrics.hint')}</Text>
+      <SimpleGrid cols={{ base: 1, sm: 2, lg: 4 }} spacing="md">
+        <StatCard label={t('exam.metrics.registrationToScheduled')} stat={data.registrationToScheduled} t={t} />
+        <StatCard label={t('exam.metrics.scheduledToAttendance')} stat={data.scheduledToAttendance} t={t} />
+        <StatCard label={t('exam.metrics.attendanceToExamStart')} stat={data.attendanceToExamStart} t={t} />
+        <StatCard label={t('exam.metrics.scheduledToExamStart')} stat={data.scheduledToExamStart} t={t} />
+      </SimpleGrid>
+    </Paper>
+  );
+}