feat: expand teaching mode with live timeline and seating quick checks

LehrerApp.Core/Models/Planning.cs

@@ -55,6 +55,7 @@ public class Lesson : IHasAttachments
     /// gepflegt. Dient nur der abgeleiteten Uhrzeit-Anzeige je Phase in <see cref="Phases"/>.
     public TimeOnly? StartTime { get; set; }
     public List<LessonPhaseStep> Phases { get; set; } = [];
+    public TeachingTimelineState? TeachingTimeline { get; set; }
     public string? Homework { get; set; }
     /// Markiert, dass die hier eingetragene Hausaufgabe in einer Folgestunde besprochen/kontrolliert
     /// wurde — treibt das Stundenplan-Badge "Hausaufgabe kontrollieren" (4.5.4).
@@ -244,3 +245,21 @@ public class ReportGrade
     public bool IsLocked { get; set; }
     public DateTime UpdatedAt { get; set; } = DateTime.UtcNow;
 }
+
+/// <summary>Live timing is separate from the original lesson plan.</summary>
+public class TeachingTimelineState
+{
+    public DateTime StartUtc { get; set; }
+    public DateTime EndUtc { get; set; }
+    public DateTime? HeldSinceUtc { get; set; }
+    public Guid? HeldPhaseId { get; set; }
+    public List<TeachingPhaseTiming> Phases { get; set; } = [];
+    public List<Guid> TransferredPhaseIds { get; set; } = [];
+}
+
+public class TeachingPhaseTiming
+{
+    public Guid PhaseId { get; set; }
+    public double Minutes { get; set; }
+    public bool ExplicitlyStarted { get; set; }
+}