Enhance staffing management with uncovered teacher tracking

- Updated `protocol.md` to clarify the concept of uncovered subjects and the number of additional teachers required.
- Introduced `teachersShort` property in the `StaffingSubject` interface to indicate how many more teachers are needed for a subject.
- Enhanced localization strings to reflect the new uncovered teacher information in both English and Russian.
- Updated the management panel UI to display the number of teachers short for each uncovered subject.
- Revised the `Uncovered` method in the staffing logic to return detailed information about uncovered subjects, including the shortfall of teachers.
- Added tests to validate the new uncovered teacher tracking functionality and ensure accurate reporting in the staffing API.
- Marked related tasks as complete in the documentation for the golden fixtures phase.

src/HSchool.People/Staffing.cs

@@ -18,6 +18,14 @@ public enum StaffingError
     NoOpening,
 }
 
+/// <summary>
+/// A subject the school cannot actually teach, and how many more teachers would cover it.
+/// </summary>
+public sealed record UncoveredSubject(SubjectDef Subject, int Assigned, int TeachersShort)
+{
+    public string DefName => Subject.DefName;
+}
+
 public sealed record StaffingOutcome(
     StaffingError Error,
     Roster Roster,
@@ -130,12 +138,32 @@ public static class Staffing
         return Round(total);
     }
 
+    /// <summary>
+    /// How many people a subject needs at the weekly cap. Primary school on a vanilla map is
+    /// eighty hours: one person cannot carry it, and the uncovered row has to say so.
+    /// </summary>
+    public static int TeachersToCover(float hours, float maxWeeklyHours)
+    {
+        if (hours <= 0f)
+        {
+            return 0;
+        }
+
+        if (maxWeeklyHours <= 0f)
+        {
+            return 1;
+        }
+
+        return (int)Math.Ceiling(hours / maxWeeklyHours);
+    }
+
     /// <summary>
     /// Subjects the school cannot actually teach: nobody is assigned them, or the people who are
     /// cannot between them carry the curriculum hours. Both read the same way to a player — the
-    /// lessons will not happen — so both belong in one list.
+    /// lessons will not happen — so both belong in one list. <see cref="UncoveredSubject.TeachersShort"/>
+    /// is how many more people it still needs.
     /// </summary>
-    public static IReadOnlyList<SubjectDef> Uncovered(DefCatalog catalog, Roster roster)
+    public static IReadOnlyList<UncoveredSubject> Uncovered(DefCatalog catalog, Roster roster)
     {
         var years = new HashSet<int>();
         foreach (var schoolClass in roster.Classes)
@@ -158,7 +186,7 @@ public static class Staffing
         }
 
         var cap = catalog.StaffingRules?.MaxWeeklyHours ?? 0f;
-        var uncovered = new List<SubjectDef>();
+        var uncovered = new List<UncoveredSubject>();
         foreach (var subject in catalog.Subjects.Values)
         {
             if (subject.Abstract || !TouchesYears(subject, years))
@@ -167,9 +195,12 @@ public static class Staffing
             }
 
             var assigned = teachers.GetValueOrDefault(subject.DefName);
-            if (assigned == 0 || (cap > 0f && SubjectHours(catalog, roster, subject.DefName) > assigned * cap))
+            var hours = SubjectHours(catalog, roster, subject.DefName);
+            var needed = TeachersToCover(hours, cap);
+            var shortfall = Math.Max(0, needed - assigned);
+            if (shortfall > 0)
             {
-                uncovered.Add(subject);
+                uncovered.Add(new UncoveredSubject(subject, assigned, shortfall));
             }
         }