feat(exams,homework,proctoring): 长期问题修复与竞品差距补齐

P1-1 跨模块直查消除：
- homework/data-access-classes.ts 移除对 exams/subjects 表的 JOIN 直查
- 改为调用 exams/data-access.getExamSubjectIdMap + school/data-access.getSubjectNameMapByIds
- school/data-access.ts 新增 getSubjectNameMapByIds 批量科目名称映射函数

P1-2 as 断言消除（exam-mode-config.tsx）：
- 移除全部 10 处 as 类型断言
- 改用 useFormContext 替代 Control prop，避免 Control<T> 不变型问题
- exam-form.tsx 调用方简化为 <ExamModeConfig />（已集成到考试表单）

P1-3 as 断言消除（proctoring-dashboard.tsx）：
- 用类型守卫函数 isProctoringEventType + toProctoringEventTypes
  替代 Object.keys(...) as ProctoringEventType[] 断言

P0-竞品倒计时（对标智学网/猿题库）：
- 新增 hooks/use-exam-countdown.ts 考试倒计时 Hook
- homework-take-view.tsx 集成限时/监考模式倒计时显示与到时自动提交
- data-access.ts 的 getStudentHomeworkTakeData 新增 examModeConfig + startedAt 字段
- types.ts 扩展 StudentHomeworkTakeData 类型
- i18n 补充 timedExam/timeRemaining/timeUpAutoSubmit 翻译键

架构文档同步：
- 004/005 更新 homework/proctoring/school/exams 模块导出与依赖关系
- 005 新增 homework.hooks.useExamCountdown 与 school.dataAccess.getSubjectNameMapByIds
- 005 依赖矩阵 homework→school 补充 getSubjectNameMapByIds

验证：tsc --noEmit 零错误，eslint 零错误（3 个预存 warning 无关）

src/modules/homework/components/homework-take-view.tsx

@@ -21,7 +21,7 @@ import {
   AlertDialogHeader,
   AlertDialogTitle,
 } from "@/shared/components/ui/alert-dialog"
-import { Clock, CheckCircle2, Save, FileText, ChevronLeft, TriangleAlert, CloudUpload, CloudOff, Check, Loader2 } from "lucide-react"
+import { Clock, CheckCircle2, Save, FileText, ChevronLeft, TriangleAlert, CloudUpload, CloudOff, Check, Loader2, Timer } from "lucide-react"
 import { formatDate, cn } from "@/shared/lib/utils"
 
 import type { StudentHomeworkTakeData } from "../types"
@@ -29,6 +29,7 @@ import { saveHomeworkAnswerAction, startHomeworkSubmissionAction, submitHomework
 import { QuestionRenderer } from "./question-renderer"
 import { parseSavedAnswer } from "../lib/question-content-utils"
 import { useDebouncedAutoSave, loadOfflineCache, clearOfflineCache } from "../hooks/use-debounced-auto-save"
+import { useExamCountdown } from "../hooks/use-exam-countdown"
 
 type HomeworkTakeViewProps = {
   assignmentId: string
@@ -195,6 +196,38 @@ export function HomeworkTakeView({ assignmentId, initialData }: HomeworkTakeView
     return false
   }).length
 
+  // P0-竞品修复：限时/监考模式倒计时
+  const examModeConfig = initialData.examModeConfig
+  const isTimedExam = canEdit
+    && examModeConfig !== null
+    && (examModeConfig.examMode === "timed" || examModeConfig.examMode === "proctored")
+    && examModeConfig.durationMinutes !== null
+    && examModeConfig.durationMinutes > 0
+    && initialData.submission?.startedAt !== null
+    && initialData.submission?.startedAt !== undefined
+
+  const countdown = useExamCountdown({
+    durationMinutes: examModeConfig?.durationMinutes ?? null,
+    startedAt: initialData.submission?.startedAt ?? null,
+    enabled: isTimedExam,
+    onExpire: () => {
+      // 到时自动提交（仅触发一次）
+      if (submissionStatus === "started" && submissionId) {
+        toast.warning(t("homework.take.timeUpAutoSubmit"))
+        void handleSubmit()
+      }
+    },
+  })
+
+  const formatCountdown = (s: { hours: number; minutes: number; seconds: number } | null): string => {
+    if (!s) return ""
+    const parts: string[] = []
+    if (s.hours > 0) parts.push(`${s.hours}h`)
+    parts.push(`${s.minutes.toString().padStart(2, "0")}m`)
+    parts.push(`${s.seconds.toString().padStart(2, "0")}s`)
+    return parts.join(" ")
+  }
+
   return (
     <div className="grid h-[calc(100vh-10rem)] grid-cols-1 gap-6 lg:grid-cols-12">
       <div className="lg:col-span-9 flex flex-col h-full overflow-hidden rounded-md border bg-card">
@@ -222,14 +255,44 @@ export function HomeworkTakeView({ assignmentId, initialData }: HomeworkTakeView
           </div>
 
           {!canEdit ? (
-            <Button onClick={handleStart} disabled={isBusy} size="sm">
-              {isBusy ? t("homework.take.starting") : t("homework.take.startAssignment")}
-            </Button>
+            <div className="flex items-center gap-3">
+              {isTimedExam && examModeConfig && (
+                <div className="flex items-center gap-1.5 rounded-md border border-orange-200 bg-orange-50 px-3 py-1.5 text-xs text-orange-700 dark:border-orange-900 dark:bg-orange-950 dark:text-orange-300">
+                  <Timer className="h-3.5 w-3.5" />
+                  <span className="font-medium">
+                    {t("homework.take.timedExam", { minutes: examModeConfig.durationMinutes ?? 0 })}
+                  </span>
+                </div>
+              )}
+              <Button onClick={handleStart} disabled={isBusy} size="sm">
+                {isBusy ? t("homework.take.starting") : t("homework.take.startAssignment")}
+              </Button>
+            </div>
           ) : (
-            <Button onClick={() => setShowSubmitConfirm(true)} disabled={isBusy} size="sm">
-              <CheckCircle2 className="mr-2 h-4 w-4" />
-              {isBusy ? t("homework.take.submitting") : t("homework.take.submitAssignment")}
-            </Button>
+            <div className="flex items-center gap-3">
+              {countdown && (
+                <div
+                  className={cn(
+                    "flex items-center gap-1.5 rounded-md border px-3 py-1.5 text-sm font-semibold tabular-nums",
+                    countdown.isExpired
+                      ? "border-destructive bg-destructive/10 text-destructive"
+                      : countdown.isUrgent
+                        ? "border-destructive bg-destructive/5 text-destructive animate-pulse"
+                        : "border-muted-foreground/20 bg-muted/50 text-foreground"
+                  )}
+                  role="timer"
+                  aria-live="polite"
+                  aria-label={t("homework.take.timeRemaining")}
+                >
+                  <Timer className="h-4 w-4" />
+                  <span>{formatCountdown(countdown)}</span>
+                </div>
+              )}
+              <Button onClick={() => setShowSubmitConfirm(true)} disabled={isBusy} size="sm">
+                <CheckCircle2 className="mr-2 h-4 w-4" />
+                {isBusy ? t("homework.take.submitting") : t("homework.take.submitAssignment")}
+              </Button>
+            </div>
           )}
         </div>