Update wire protocol to version 6 and enhance timetable functionality

- Bumped the wire protocol version to 6, reflecting changes in the communication structure.
- Expanded the timetable API with new endpoints for fetching and managing lesson schedules, including `GET /api/schools/{id}/timetable` and `POST /api/schools/{id}/timetable/pin`.
- Updated the protocol documentation to include detailed descriptions of the new timetable features and message structures.
- Enhanced the client-side implementation to support the new timetable functionalities, including lesson pinning and unpinning.
- Revised server-side logic to handle timetable operations and ensure proper integration with existing school management features.
- Added tests to validate the new timetable functionalities and ensure robustness in handling lesson data.

src/HSchool.Schedule/TimetableClock.cs

@@ -0,0 +1,38 @@
+using HSchool.Content;
+
+namespace HSchool.Schedule;
+
+/// <summary>
+/// Which lessons are happening at a game instant. Breaks, nights, weekends and holidays are empty
+/// — occupancy is derived, never stored.
+/// </summary>
+public static class TimetableClock
+{
+    public static IReadOnlyList<LessonPlacement> OccurringAt(
+        Timetable table,
+        DefCatalog catalog,
+        DateTime time,
+        int weekDays)
+    {
+        ArgumentNullException.ThrowIfNull(table);
+        var slot = SchoolDay.At(catalog, time, weekDays);
+        if (slot.Kind != DaySlotKind.Lesson)
+        {
+            return [];
+        }
+
+        var day = SchoolDay.WeekdayIndex(time);
+        return table.Lessons
+            .Where(lesson => lesson.Day == day && lesson.Period == slot.Index)
+            .ToArray();
+    }
+
+    public static OccupancyKey Key(DefCatalog catalog, DateTime time, int weekDays)
+    {
+        var utc = DateTime.SpecifyKind(time, DateTimeKind.Utc);
+        var slot = SchoolDay.At(catalog, utc, weekDays);
+        return new OccupancyKey(DateOnly.FromDateTime(utc), slot.Kind, slot.Index);
+    }
+}
+
+public readonly record struct OccupancyKey(DateOnly Day, DaySlotKind Kind, int Index);