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.

tests/HSchool.People.Tests/StaffingTests.cs

@@ -232,6 +232,28 @@ public class StaffingTests
         Assert.Contains(Staffing.Uncovered(catalog, assigned.Roster), subject => subject.DefName == "PrimarySchool");
     }
 
+    [Fact]
+    public void PrimarySchool_OnVanillaMap_NeedsThreeTeachers_AndASecondDoesNotCloseIt()
+    {
+        var (catalog, map, roster, pool) = Fresh();
+        var rules = catalog.StaffingRules!;
+        Assert.Equal(80f, Staffing.SubjectHours(catalog, roster, "PrimarySchool"));
+        Assert.Equal(3, Staffing.TeachersToCover(80f, rules.MaxWeeklyHours));
+
+        var empty = Staffing.Uncovered(catalog, roster).Single(subject => subject.DefName == "PrimarySchool");
+        Assert.Equal(3, empty.TeachersShort);
+
+        var outcome = new StaffingOutcome(StaffingError.None, roster, pool, 0, 0, 0, 0);
+        outcome = HireAndAssign(catalog, map, outcome, "PrimarySchool");
+        Assert.Equal(2, Staffing.Uncovered(catalog, outcome.Roster).Single(subject => subject.DefName == "PrimarySchool").TeachersShort);
+
+        outcome = HireAndAssign(catalog, map, outcome, "PrimarySchool");
+        Assert.Equal(1, Staffing.Uncovered(catalog, outcome.Roster).Single(subject => subject.DefName == "PrimarySchool").TeachersShort);
+
+        outcome = HireAndAssign(catalog, map, outcome, "PrimarySchool");
+        Assert.DoesNotContain(Staffing.Uncovered(catalog, outcome.Roster), subject => subject.DefName == "PrimarySchool");
+    }
+
     [Fact]
     public void PeopleJson_RoundTripsHiredStaffAndSubjects()
     {
@@ -274,6 +296,20 @@ public class StaffingTests
         return (catalog, map, roster, pool);
     }
 
+    private static StaffingOutcome HireAndAssign(
+        DefCatalog catalog,
+        MapLayout map,
+        StaffingOutcome current,
+        string subject)
+    {
+        var applicant = current.Pool.Applicants[0];
+        var hired = Staffing.Hire(catalog, map, current.Roster, current.Pool, applicant.Person.Id, Staffing.TeacherPosition, 500_000f);
+        Assert.Equal(StaffingError.None, hired.Error);
+        var assigned = Staffing.AssignSubject(catalog, hired.Roster, hired.Pool, applicant.Person.Id, subject, 500_000f);
+        Assert.Equal(StaffingError.None, assigned.Error);
+        return assigned;
+    }
+
     private static Applicant WithAsk(Applicant applicant, float hourlyAsk) =>
         applicant with { HourlyWageAsk = hourlyAsk };
 }