fix(exam): guard question assignment once the paper is locked

The detail page fired assign/draw requests blind and surfaced the raw
backend key to the user — a locked paper showed up as the literal string
"paper_locked_after_registration" in a toast.

Manage Questions is now disabled once any candidate has registered, with a
tooltip and badge explaining why; both the manual assign and the random draw
live behind that modal, so one guard covers the same ground the backend's
assertPaperEditable does. The empty-paper alert now explains the deadlock
instead of telling the user to click a button that will fail, and both
error handlers translate paper_locked_after_registration in case someone
registers while the modal is open.

Registrations come from the query ExamCandidatesPanel already runs on this
page, so RTK Query serves it from cache rather than issuing a second request.

apps/backoffice/src/app/features/exam/pages/ExamDetailPage.tsx

@@ -22,6 +22,7 @@ import {
   TextInput,
   ThemeIcon,
   Box,
+  Tooltip,
   rem,
 } from "@mantine/core";
 import { useDisclosure } from "@mantine/hooks";
@@ -48,6 +49,7 @@ import {
   useUpdateExamMutation,
   useAssignQuestionsMutation,
   useSelectRandomQuestionsMutation,
+  useGetExamRegistrationsQuery,
 } from '../api/exam-api';
 import { useGetQuestionsQuery } from '../../question/api/question-api';
 import { useGetCertificationsQuery } from '../../certification/api/certification-api';
@@ -114,6 +116,12 @@ export function ExamDetailPage() {
   const [selectRandom, { isLoading: isDrawing }] = useSelectRandomQuestionsMutation();
 
   const { data: exam, isLoading, isError } = useGetExamQuery(id ?? '', { skip: !id });
+  // The backend locks the paper the moment the first candidate registers
+  // (ExamService.assertPaperEditable) — every candidate must sit the same
+  // paper. Same query ExamCandidatesPanel already runs, so RTK Query serves
+  // it from cache rather than issuing a second request.
+  const { data: registrations } = useGetExamRegistrationsQuery(id ?? '', { skip: !id });
+  const paperLocked = (registrations?.length ?? 0) > 0;
   const { data: qRes } = useGetQuestionsQuery();
   const { data: certRes } = useGetCertificationsQuery();
   const allQuestions = qRes?.items ?? [];
@@ -183,7 +191,9 @@ export function ExamDetailPage() {
     } catch (error) {
       const key = extractErrorMessage(error, t('exam.randomError'));
       notify.error(
-        key.startsWith('insufficient_approved_questions')
+        key === 'paper_locked_after_registration'
+          ? t('exam.paperLockedHint', { count: registrations?.length ?? 0 })
+          : key.startsWith('insufficient_approved_questions')
           ? `${t('exam.notEnoughApproved')} (${key.split(':')[1] ?? ''})`
           : key.startsWith('paper_cannot_reach_cutting_point')
             ? t('exam.cannotReachCuttingPoint', {
@@ -204,7 +214,9 @@ export function ExamDetailPage() {
     } catch (error) {
       const key = extractErrorMessage(error, 'Failed to assign questions');
       notify.error(
-        key.startsWith('question_not_approved')
+        key === 'paper_locked_after_registration'
+          ? t('exam.paperLockedHint', { count: registrations?.length ?? 0 })
+          : key.startsWith('question_not_approved')
           ? t('question.qc.onlyApprovedUsable')
           : key.startsWith('paper_cannot_reach_cutting_point')
             ? t('exam.cannotReachCuttingPoint', {
@@ -456,19 +468,45 @@ export function ExamDetailPage() {
             {t("exam.detail.questionsSection", { pts: totalPoints })}
           </Title>
           <RequirePermission anyOf={[LICENSE_PERMISSIONS.MANAGE_EXAMS]} hideOnly>
+            <Group gap="xs">
+              {paperLocked && (
+                <Badge size="sm" variant="light" color="gray">
+                  {t("exam.paperLocked")}
+                </Badge>
+              )}
+              <Tooltip
+                label={t("exam.paperLockedHint", {
+                  count: registrations?.length ?? 0,
+                })}
+                disabled={!paperLocked}
+                multiline
+                w={280}
+              >
+                {/* Wrapped: a disabled Mantine Button fires no pointer events,
+                    so the tooltip needs an enabled element to hang off. */}
+                <Box>
                   <Button
                     variant="light"
                     size="xs"
                     leftSection={<IconPlus size={14} />}
                     onClick={openAssignModal}
+                    disabled={paperLocked}
                   >
                     {t("exam.manageQuestions")}
                   </Button>
+                </Box>
+              </Tooltip>
+            </Group>
           </RequirePermission>
         </Group>
         {(exam.questions ?? []).length === 0 ? (
-          <Alert color="gray" icon={<IconInfoCircle size={16} />}>
-            {t("exam.noQuestionsAssigned")}
+          <Alert
+            color={paperLocked ? "red" : "gray"}
+            icon={<IconInfoCircle size={16} />}
+          >
+            {paperLocked
+              ? t("exam.paperLockedHint", { count: registrations?.length ?? 0 })
+              : t("exam.noQuestionsAssigned")}
           </Alert>
         ) : (
           <Stack gap="md">

apps/backoffice/src/app/i18n/locales/am.ts

@@ -387,6 +387,9 @@ export const am: Translations = {
     notEnoughApproved: "ለዚህ ትምህርት በቂ የጸደቁ ጥያቄዎች የሉም።",
     cannotReachCuttingPoint:
       "ይህ ወረቀት የማለፊያ ነጥቡን ሊደርስ አይችልም (ከፍተኛ {{max}}፣ የማለፊያ ነጥብ {{cuttingPoint}})። ተጨማሪ ወይም ከፍ ያለ ነጥብ ያላቸው ጥያቄዎችን ጨምር፣ ወይም የማለፊያ ነጥቡን ቀንስ።",
+    paperLocked: "ወረቀቱ ተቆልፏል",
+    paperLockedHint:
+      "ለዚህ ፈተና {{count}} ተፈታኝ(ዎች) ተመዝግበዋል። ሁሉም ተፈታኞች አንድ ዓይነት ወረቀት መፈተን ስላለባቸው ጥያቄዎቹ ከዚህ በኋላ አይቀየሩም።",
   },
 
   country: {

apps/backoffice/src/app/i18n/locales/en.ts

@@ -386,6 +386,9 @@ export const en = {
       'Not enough approved questions in the bank for this subject.',
     cannotReachCuttingPoint:
       'This paper cannot reach the passing mark (max {{max}}, pass mark {{cuttingPoint}}). Add more/higher-point questions, or lower the cutting point.',
+    paperLocked: 'Paper locked',
+    paperLockedHint:
+      '{{count}} candidate(s) have registered for this session. Every candidate must sit the same paper, so questions can no longer be changed.',
   },
 
   country: {