Add rating snapshots, percentile, and exam readiness to the dashboard API

Backend half of the dashboard stat-card redesign. Three new data
points the old DashboardResponse had no way to compute:

- Week-over-week rating deltas: UserRating/CcsUserRating only ever
  stored the current Elo (mutated in place, UpdatedUtc just means
  "last touched"), so there was no way to know what a rating was 7
  days ago. Added UserRatingSnapshot (new collection, unique on
  UserId+DateUtc) and UserRatingSnapshotService, a BackgroundService
  following AnswerStatisticsMaintenanceService's exact shape (a
  PeriodicTimer plus a Mongo lease so replicas behind the HPA don't
  race), writing one snapshot per user per day. No historical
  backfill - deltas are simply null for a user's first ~7 days after
  this ships, which the DTO represents honestly via nullable ints
  rather than a fake "+0".
- Percentile rank: DashboardStore now counts how many users have a
  higher OverallElo/Elo than the current user out of the total.
- Exam Readiness + projected pass rate: reuses the existing, tested
  IRT-based ExamSimulationScore.PassProbability (a real normal-CDF
  estimate of scoring >=200, computed in ExamSimulationScoring.Calculate)
  rather than inventing a new prediction model. DashboardStore pulls
  the latest completed simulation's score directly and maps
  PassProbability to a High/Medium/Low label via tunable thresholds.
- Average Score's "+6% vs last 100" needed no new data source at all -
  just one more slice (Skip(100).Take(100)) over the QuestionAttempts
  already loaded for FirstAttemptAccuracy.

Added DashboardStore.Percentile/ReadinessLabel as pure static helpers
(matching the existing Percentage/CalculateCurrentStreak pattern) and
unit tests for both. Full backend suite: 165 passed, 0 failed.

api/QuestionsApi.Tests/DashboardTests.cs

@@ -100,7 +100,8 @@ public sealed class DashboardTests
             HistoryStartedUtc = baselineDate
         };
 
-        var result = DashboardStore.BuildPerformanceTrend(attempts, rating, today);
+        var result = DashboardStore.BuildPerformanceTrend(
+            attempts, rating, Array.Empty<CcsAttempt>(), new CcsUserRating(), today);
 
         Assert.Equal(30, result.Count);
         Assert.Null(result[^4].QuestionBankRating);
@@ -113,6 +114,39 @@ public sealed class DashboardTests
         Assert.Equal(100, result[^1].Accuracy);
     }
 
+    [Fact]
+    public void TrendCarriesCcsRatingForwardIndependentlyOfQuestionBankRating()
+    {
+        var today = new DateTime(2026, 7, 25, 0, 0, 0, DateTimeKind.Utc);
+        var baselineDate = today.AddDays(-2).AddHours(8);
+        var rating = new UserRating();
+        var ccsRating = new CcsUserRating
+        {
+            Elo = 1050,
+            HistoryBaselineElo = 1000,
+            HistoryStartedUtc = baselineDate
+        };
+        var ccsAttempts = new[]
+        {
+            RatedCcsAttempt("one", today.AddDays(-1).AddHours(9), 1030),
+            RatedCcsAttempt("two", today.AddHours(10), 1050)
+        };
+
+        var result = DashboardStore.BuildPerformanceTrend(
+            Array.Empty<QuestionAttempt>(), rating, ccsAttempts, ccsRating, today);
+
+        Assert.Equal(30, result.Count);
+        Assert.Equal(1000, result[^3].CcsRating);
+        Assert.Equal(1030, result[^2].CcsRating);
+        Assert.Equal(1050, result[^1].CcsRating);
+    }
+
+    private static CcsAttempt RatedCcsAttempt(string caseExternalId, DateTime appliedUtc, int userElo) => new()
+    {
+        CaseExternalId = caseExternalId,
+        Rating = new CcsRatingChange { Rated = true, UserElo = userElo, AppliedUtc = appliedUtc }
+    };
+
     private static QuestionAttempt Attempt(
         string questionId,
         bool correct,
@@ -134,4 +168,35 @@ public sealed class DashboardTests
         ExternalId = system,
         System = system
     };
+
+    [Fact]
+    public void PercentileReturnsNullWithNoUsers()
+    {
+        Assert.Null(DashboardStore.Percentile(0, 0));
+    }
+
+    [Fact]
+    public void PercentileComputesTopPercentFromUsersRatedHigher()
+    {
+        // 18 of 100 users rate higher than this user - "top 18%"
+        Assert.Equal(18, DashboardStore.Percentile(18, 100));
+    }
+
+    [Fact]
+    public void PercentileNeverReturnsZero()
+    {
+        // Even the single best-rated user should read as "top 1%", not "top 0%"
+        Assert.Equal(1, DashboardStore.Percentile(0, 100));
+    }
+
+    [Theory]
+    [InlineData(0.85, "High")]
+    [InlineData(0.7, "High")]
+    [InlineData(0.55, "Medium")]
+    [InlineData(0.4, "Medium")]
+    [InlineData(0.1, "Low")]
+    public void ReadinessLabelUsesPassProbabilityThresholds(double passProbability, string expected)
+    {
+        Assert.Equal(expected, DashboardStore.ReadinessLabel(passProbability));
+    }
 }