feat: time-in-stage analytics + pipeline-driven funnel

- New pure StageAnalytics.TimeInStage: median days jobs have spent in
  each active pipeline stage (entry time from the last StatusChanged
  event into that stage, else applied date). Closed/success stages
  excluded since 'how long stuck' only applies to actionable stages.
- analytics-overview now derives the funnel from JobPipeline (includes
  the previously-omitted Waiting stage, normalizes legacy spellings) and
  returns TimeInStage.
- 4 unit tests; full backend suite green (124).

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

JobTrackerApi/Services/StageAnalytics.cs

@@ -0,0 +1,45 @@
+namespace JobTrackerApi.Services
+{
+    public sealed record StageDurationPoint(string Stage, int Order, double MedianDays, int Count);
+
+    /// <summary>One job's position: its canonical stage and when it entered that stage.</summary>
+    public sealed record StageOccupancy(string Status, DateTime EnteredStageAtUtc);
+
+    /// <summary>
+    /// Pure time-in-stage analytics: for each active pipeline stage, the median number of days
+    /// the jobs currently sitting there have been waiting. Closed stages (Rejected/Ghosted) and
+    /// the terminal success stage (Offer) are excluded — "how long has this been stuck" only
+    /// makes sense for stages you still act on.
+    /// </summary>
+    public static class StageAnalytics
+    {
+        public static List<StageDurationPoint> TimeInStage(IEnumerable<StageOccupancy> jobs, DateTime nowUtc)
+        {
+            var byStage = jobs
+                .Select(j => (Stage: JobPipeline.Normalize(j.Status), Days: Math.Max(0, (nowUtc - j.EnteredStageAtUtc).TotalDays)))
+                .Where(x => JobPipeline.Stages.Any(s => s.Key == x.Stage && s.Category == PipelineCategory.Active))
+                .GroupBy(x => x.Stage);
+
+            var points = new List<StageDurationPoint>();
+            foreach (var group in byStage)
+            {
+                var days = group.Select(x => x.Days).OrderBy(x => x).ToList();
+                points.Add(new StageDurationPoint(
+                    Stage: group.Key,
+                    Order: JobPipeline.OrderOf(group.Key),
+                    MedianDays: Median(days),
+                    Count: days.Count));
+            }
+
+            return points.OrderBy(p => p.Order).ToList();
+        }
+
+        private static double Median(IReadOnlyList<double> sorted)
+        {
+            if (sorted.Count == 0) return 0;
+            var mid = sorted.Count / 2;
+            var median = sorted.Count % 2 == 0 ? (sorted[mid - 1] + sorted[mid]) / 2d : sorted[mid];
+            return Math.Round(median, 1);
+        }
+    }
+}