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.Server/Api/PeopleModels.cs

@@ -196,7 +196,8 @@ internal sealed record UncoveredSubjectResponse(
     string Label,
     int GradeMin,
     int GradeMax,
-    int HoursPerWeek);
+    int HoursPerWeek,
+    int TeachersShort);
 
 internal sealed record ApplicantResponse(
     string Id,
@@ -241,12 +242,13 @@ internal static class StaffingMapper
         var uncovered = catalog is null
             ? Array.Empty<UncoveredSubjectResponse>()
             : Staffing.Uncovered(catalog, roster)
-                .Select(subject => new UncoveredSubjectResponse(
-                    subject.DefName,
-                    catalog.Label(locale, subject),
-                    subject.Grades.Min,
-                    subject.Grades.Max,
-                    subject.HoursPerWeek))
+                .Select(row => new UncoveredSubjectResponse(
+                    row.Subject.DefName,
+                    catalog.Label(locale, row.Subject),
+                    row.Subject.Grades.Min,
+                    row.Subject.Grades.Max,
+                    row.Subject.HoursPerWeek,
+                    row.TeachersShort))
                 .ToArray();
 
         var applicants = pool.Applicants
@@ -286,7 +288,8 @@ internal static class StaffingMapper
                     catalog.Label(locale, def),
                     def.Grades.Min,
                     def.Grades.Max,
-                    def.HoursPerWeek))
+                    def.HoursPerWeek,
+                    0))
                 .ToArray();
 
         return new StaffingResponse(allocated, payroll, remaining, uncovered, applicants, staff, positions, subjects);