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/Controllers/JobApplicationsController.cs

@@ -2023,13 +2023,15 @@ Canonical profile:
         public sealed record CompanyActivityPoint(int CompanyId, string Company, int Count, int Responses, double ResponseRate);
         public sealed record TagTrendSeries(string Tag, List<int> Counts);
         public sealed record TagTrendPoint(string Month, List<int> Counts);
+        public sealed record StageDurationDto(string Stage, double MedianDays, int Count);
         public sealed record AnalyticsOverviewDto(
             List<FunnelStagePoint> Funnel,
             List<ResponseRatePoint> ResponseRateBySource,
             List<CompanyActivityPoint> TopCompanies,
             double? MedianDaysToFirstResponse,
             int TotalResponses,
-            int TotalActive
+            int TotalActive,
+            List<StageDurationDto> TimeInStage
         );
         public sealed record DuplicateCandidateDto(int Id, string JobTitle, string Company, string? JobUrl, string Status, DateTime DateApplied, string Reason);
         public sealed record DuplicateCheckResult(bool HasDuplicates, List<DuplicateCandidateDto> Matches);
@@ -2803,16 +2805,14 @@ Candidate master CV:
                 .Where(j => !j.IsDeleted)
                 .ToListAsync(cancellationToken);
 
-            var funnelMap = new Dictionary<string, int>
-            {
-                ["Applied"] = activeJobs.Count(j => string.Equals(j.Status, "Applied", StringComparison.OrdinalIgnoreCase)),
-                ["Interview"] = activeJobs.Count(j => string.Equals(j.Status, "Interview", StringComparison.OrdinalIgnoreCase) || string.Equals(j.Status, "Interviewing", StringComparison.OrdinalIgnoreCase)),
-                ["Offer"] = activeJobs.Count(j => string.Equals(j.Status, "Offer", StringComparison.OrdinalIgnoreCase)),
-                ["Rejected"] = activeJobs.Count(j => string.Equals(j.Status, "Rejected", StringComparison.OrdinalIgnoreCase)),
-                ["Ghosted"] = activeJobs.Count(j => string.Equals(j.Status, "Ghosted", StringComparison.OrdinalIgnoreCase)),
-            };
-
-            var funnel = funnelMap.Select(x => new FunnelStagePoint(x.Key, x.Value)).ToList();
+            // Funnel = distribution across canonical stages, driven by the pipeline (one source
+            // of truth, so it includes every stage and normalizes legacy spellings).
+            var normalizedByStage = activeJobs
+                .GroupBy(j => JobPipeline.Normalize(j.Status))
+                .ToDictionary(g => g.Key, g => g.Count());
+            var funnel = JobPipeline.Stages
+                .Select(stage => new FunnelStagePoint(stage.Key, normalizedByStage.TryGetValue(stage.Key, out var c) ? c : 0))
+                .ToList();
 
             var responseRateBySource = activeJobs
                 .GroupBy(j => string.IsNullOrWhiteSpace(j.Company?.Source) ? "Unknown source" : j.Company!.Source!.Trim())
@@ -2856,13 +2856,46 @@ Candidate master CV:
                     : Math.Round(responseDays[mid], 1);
             }
 
+            // Time-in-stage: for each active job, when did it enter its current stage? Use the most
+            // recent StatusChanged event into that stage, else its applied date.
+            var activeIds = activeJobs.Select(j => j.Id).ToList();
+            var statusChanges = await _db.JobEvents
+                .AsNoTracking()
+                .Where(e => e.Type == "StatusChanged" && activeIds.Contains(e.JobApplicationId))
+                .Select(e => new { e.JobApplicationId, e.NewValue, e.At })
+                .ToListAsync(cancellationToken);
+
+            var lastEntryByJob = statusChanges
+                .GroupBy(e => e.JobApplicationId)
+                .ToDictionary(g => g.Key, g => g.ToList());
+
+            var occupancy = activeJobs.Select(job =>
+            {
+                var current = JobPipeline.Normalize(job.Status);
+                DateTime enteredAt = job.DateApplied;
+                if (lastEntryByJob.TryGetValue(job.Id, out var changes))
+                {
+                    var lastIntoCurrent = changes
+                        .Where(e => JobPipeline.Normalize(e.NewValue) == current)
+                        .OrderByDescending(e => e.At)
+                        .FirstOrDefault();
+                    if (lastIntoCurrent is not null) enteredAt = lastIntoCurrent.At;
+                }
+                return new StageOccupancy(current, enteredAt.ToUniversalTime());
+            });
+
+            var timeInStage = StageAnalytics.TimeInStage(occupancy, DateTime.UtcNow)
+                .Select(p => new StageDurationDto(p.Stage, p.MedianDays, p.Count))
+                .ToList();
+
             return Ok(new AnalyticsOverviewDto(
                 Funnel: funnel,
                 ResponseRateBySource: responseRateBySource,
                 TopCompanies: topCompanies,
                 MedianDaysToFirstResponse: medianDays,
                 TotalResponses: activeJobs.Count(j => j.ResponseReceived || j.ResponseDate is not null),
-                TotalActive: activeJobs.Count
+                TotalActive: activeJobs.Count,
+                TimeInStage: timeInStage
             ));
         }