Add In-progress stat card and live list to mobile Home

Surface actively-running sessions on the phone home dashboard: a fourth
"In progress" stat card and a list pinned above the to-dos. Both share one
definition (live sessions with status .running), and list rows link into the
session transcript.

Co-Authored-By: Claude Opus 4.8 <[email protected]>

NucleicRemote/NucleicRemote/Views/HomeView.swift

@@ -8,6 +8,12 @@ struct HomeView: View {
     @EnvironmentObject var store: RemoteStore
 
     private var counts: DashboardCounts { store.dashboard.counts }
+
+    /// Sessions actively working a turn — drives both the "In progress" stat card and the
+    /// live list pinned above the to-dos.
+    private var running: [WireSessionSummary] {
+        store.liveSessions.filter { $0.status == .running }.sorted { $0.updatedAt > $1.updatedAt }
+    }
     private var activityByDay: [Date: Int] {
         Dictionary(store.dashboard.activity.map { (Calendar.current.startOfDay(for: $0.day), $0.count) },
                    uniquingKeysWith: +)
@@ -56,6 +62,8 @@ struct HomeView: View {
                     .frame(maxWidth: .infinity, alignment: .leading)
                     .card()
 
+                    if !running.isEmpty { InProgressSessions(sessions: running) }
+
                     QuickTodos()
 
                     StartChatComposer()
@@ -78,12 +86,39 @@ struct HomeView: View {
     private var statCards: some View {
         HStack(spacing: 12) {
             StatCard(value: counts.projects, label: "Projects", icon: "folder")
+            StatCard(value: running.count, label: "In progress", icon: "circle.lefthalf.filled")
             StatCard(value: counts.activeChats, label: "Active", icon: "bolt")
             StatCard(value: counts.messages, label: "Messages", icon: "paperplane")
         }
     }
 }
 
+/// Live peek at sessions actively running a turn, pinned above the to-do list on Home. Tapping
+/// a row drops into the session transcript.
+private struct InProgressSessions: View {
+    let sessions: [WireSessionSummary]
+
+    var body: some View {
+        VStack(alignment: .leading, spacing: 10) {
+            HStack {
+                Text("In progress").font(.headline)
+                Spacer()
+                Text("\(sessions.count)").foregroundStyle(.secondary)
+            }
+            ForEach(sessions.prefix(4), id: \.sessionID) { summary in
+                NavigationLink {
+                    SessionDetailView(sessionID: summary.sessionID)
+                } label: {
+                    SessionRow(summary: summary)
+                }
+                .buttonStyle(.plain)
+            }
+        }
+        .frame(maxWidth: .infinity, alignment: .leading)
+        .card()
+    }
+}
+
 private struct StatCard: View {
     let value: Int
     let label: String