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/RosterFingerprint.cs

@@ -0,0 +1,78 @@
+namespace HSchool.People.Tests;
+
+/// <summary>
+/// One line per class and person, sorted, so a generator change shows up as the first
+/// mismatched line instead of "the snapshots differ".
+/// </summary>
+internal static class RosterFingerprint
+{
+    public static string Format(Roster roster, int seed, string nameSet, string native)
+    {
+        var lines = new List<string>
+        {
+            $"# seed={seed} nameset={nameSet} native={native} people={roster.People.Count} classes={roster.Classes.Count}",
+        };
+
+        foreach (var schoolClass in roster.Classes.OrderBy(row => row.Id, StringComparer.Ordinal))
+        {
+            var pupils = string.Join(',', schoolClass.PupilIds.Order(StringComparer.Ordinal));
+            lines.Add(
+                $"class {schoolClass.Id} year={schoolClass.Year} letter={schoolClass.Letter} room={schoolClass.RoomId} capacity={schoolClass.Capacity} pupils={pupils}");
+        }
+
+        foreach (var person in roster.People.OrderBy(row => row.Id, StringComparer.Ordinal))
+        {
+            lines.Add(PersonLine(person));
+        }
+
+        return string.Join('\n', lines) + '\n';
+    }
+
+    public static void AssertEqual(string expected, string actual)
+    {
+        var left = expected.Replace("\r\n", "\n", StringComparison.Ordinal).Split('\n');
+        var right = actual.Replace("\r\n", "\n", StringComparison.Ordinal).Split('\n');
+        var count = Math.Min(left.Length, right.Length);
+        for (var i = 0; i < count; i++)
+        {
+            if (!string.Equals(left[i], right[i], StringComparison.Ordinal))
+            {
+                Assert.Fail($"first mismatch at line {i + 1}\nexpected: {left[i]}\nactual:   {right[i]}");
+            }
+        }
+
+        if (left.Length != right.Length)
+        {
+            Assert.Fail($"line count {left.Length} vs {right.Length}");
+        }
+    }
+
+    private static string PersonLine(Person person)
+    {
+        var roles = string.Join(',', Roles(person));
+        var traits = string.Join(',', person.Traits.Order(StringComparer.Ordinal));
+        var skills = string.Join(
+            ',',
+            person.Skills.OrderBy(pair => pair.Key, StringComparer.Ordinal).Select(pair => $"{pair.Key}={pair.Value}"));
+        return
+            $"person {person.Id} {person.Name.Full} female={person.Female} roles={roles} class={person.ClassId ?? "-"} born={person.BirthDate:yyyy-MM-dd} traits={traits} skills={skills}";
+    }
+
+    private static IEnumerable<string> Roles(Person person)
+    {
+        if (person.IsStudent)
+        {
+            yield return "student";
+        }
+
+        if (person.IsStaff)
+        {
+            yield return "staff";
+        }
+
+        if (person.IsParent)
+        {
+            yield return "parent";
+        }
+    }
+}