空闲教室与场地预约占用检查，现在对新发布课表优先查询 PublishedScheduleOccurrences。

查询直接按“学期 + 周次 + 星期 + 节次”命中投影索引，不再扫描周期规则并在应用层判断单双周。
历史已发布课表若尚未生成投影，自动回退到原规则表，兼容现有数据。
调停课审批后会重建受影响教学任务的已发布投影，因此占用结果同步更新。

src/Jiaowu.Api/Infrastructure/Timetables/ClassroomReservationAvailabilityService.cs

@@ -17,33 +17,34 @@ public sealed class ClassroomReservationAvailabilityService(AppDbContext db)
         var occupiedIds = new HashSet<Guid>();
         var (week, dayOfWeek) = ResolveTeachingWeek(term, reservationDate);
 
-        var scheduleEntries = await db.ScheduleEntries.AsNoTracking()
-            .Where(entry =>
-                entry.ClassroomId.HasValue &&
-                entry.SchedulePlan!.AcademicTermId == term.Id &&
-                entry.SchedulePlan.Status == SchedulePlanStatus.Published &&
-                entry.DayOfWeek == dayOfWeek &&
-                entry.StartWeek <= week &&
-                entry.EndWeek >= week &&
-                entry.StartPeriod < startPeriod + periodCount &&
-                startPeriod < entry.StartPeriod + entry.PeriodCount)
-            .Select(entry => new
-            {
-                entry.ClassroomId,
-                entry.WeekPattern,
-                entry.StartPeriod,
-                entry.PeriodCount
-            })
-            .ToListAsync(cancellationToken);
-        foreach (var entry in scheduleEntries.Where(entry =>
-                     FreeClassroomRules.MatchesWeek(entry.WeekPattern, week) &&
-                     FreeClassroomRules.PeriodsOverlap(
-                         startPeriod,
-                         periodCount,
-                         entry.StartPeriod,
-                         entry.PeriodCount)))
+        var hasProjection = await db.PublishedScheduleOccurrences.AsNoTracking()
+            .AnyAsync(entry => entry.AcademicTermId == term.Id, cancellationToken);
+        if (hasProjection)
         {
-            occupiedIds.Add(entry.ClassroomId!.Value);
+            var projectedRoomIds = await db.PublishedScheduleOccurrences.AsNoTracking()
+                .Where(entry => entry.AcademicTermId == term.Id && entry.Week == week &&
+                    entry.DayOfWeek == dayOfWeek && entry.ClassroomId.HasValue &&
+                    entry.StartPeriod < startPeriod + periodCount &&
+                    startPeriod < entry.StartPeriod + entry.PeriodCount)
+                .Select(entry => entry.ClassroomId!.Value)
+                .ToListAsync(cancellationToken);
+            occupiedIds.UnionWith(projectedRoomIds);
+        }
+        else
+        {
+            var scheduleEntries = await db.ScheduleEntries.AsNoTracking()
+                .Where(entry => entry.ClassroomId.HasValue &&
+                    entry.SchedulePlan!.AcademicTermId == term.Id &&
+                    entry.SchedulePlan.Status == SchedulePlanStatus.Published &&
+                    entry.DayOfWeek == dayOfWeek && entry.StartWeek <= week &&
+                    entry.EndWeek >= week && entry.StartPeriod < startPeriod + periodCount &&
+                    startPeriod < entry.StartPeriod + entry.PeriodCount)
+                .Select(entry => new { entry.ClassroomId, entry.WeekPattern, entry.StartPeriod, entry.PeriodCount })
+                .ToListAsync(cancellationToken);
+            foreach (var entry in scheduleEntries.Where(entry =>
+                         FreeClassroomRules.MatchesWeek(entry.WeekPattern, week) &&
+                         FreeClassroomRules.PeriodsOverlap(startPeriod, periodCount, entry.StartPeriod, entry.PeriodCount)))
+                occupiedIds.Add(entry.ClassroomId!.Value);
         }
 
         var examRoomIds = await db.ExamSessions.AsNoTracking()