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/data-access.ts

@@ -12,7 +12,7 @@ import {
   homeworkSubmissions,
 } from "@/shared/db/schema"
 import { getStudentIdsByClassId, getStudentIdsByClassIds } from "@/modules/classes/data-access"
-import { getExamIdsByGradeIds, getExamSubjectIdMap } from "@/modules/exams/data-access"
+import { getExamIdsByGradeIds, getExamSubjectIdMap, getExamForProctoringCrossModule } from "@/modules/exams/data-access"
 import { getSubjectOptions } from "@/modules/school/data-access"
 
 import type {
@@ -935,6 +935,24 @@ export const getStudentHomeworkTakeData = cache(async (assignmentId: string, stu
     }
   }
 
+  // P0-竞品修复：获取考试模式配置（仅当作业关联考试时）
+  let examModeConfig: StudentHomeworkTakeData["examModeConfig"] = null
+  if (assignment.sourceExamId) {
+    const examConfig = await getExamForProctoringCrossModule(assignment.sourceExamId)
+    if (examConfig) {
+      examModeConfig = {
+        examMode: (examConfig.examMode === "timed" || examConfig.examMode === "proctored" || examConfig.examMode === "homework")
+          ? examConfig.examMode
+          : "homework",
+        durationMinutes: examConfig.durationMinutes,
+        shuffleQuestions: examConfig.shuffleQuestions ?? false,
+        allowLateStart: examConfig.allowLateStart ?? false,
+        lateStartGraceMinutes: examConfig.lateStartGraceMinutes ?? 0,
+        antiCheatEnabled: examConfig.antiCheatEnabled ?? false,
+      }
+    }
+  }
+
   return {
     assignment: {
       id: assignment.id,
@@ -946,6 +964,7 @@ export const getStudentHomeworkTakeData = cache(async (assignmentId: string, stu
       lateDueAt: assignment.lateDueAt ? assignment.lateDueAt.toISOString() : null,
       maxAttempts: assignment.maxAttempts,
     },
+    examModeConfig,
     submission: latestSubmission
       ? {
           id: latestSubmission.id,
@@ -953,6 +972,7 @@ export const getStudentHomeworkTakeData = cache(async (assignmentId: string, stu
           attemptNo: latestSubmission.attemptNo,
           submittedAt: latestSubmission.submittedAt ? latestSubmission.submittedAt.toISOString() : null,
           score: latestSubmission.score ?? null,
+          startedAt: latestSubmission.createdAt ? latestSubmission.createdAt.toISOString() : null,
         }
       : null,
     questions: assignmentQuestions.map((aq) => {