feat(mission-control): show running Worker operations in a Running now section

Registry of active verify/merge/rebase/worktree-creation operations in the Worker,
GetActiveOperations snapshot + OperationStarted/OperationEnded hub events, and a
Running now section in Mission Control with ticking elapsed time.

Co-Authored-By: Claude Sonnet 5.5 <noreply@anthropic.com>

tests/ClaudeDo.Worker.Tests/Lifecycle/RunningOperationRegistryTests.cs

@@ -0,0 +1,55 @@
+using ClaudeDo.Worker.Hub;
+using ClaudeDo.Worker.Lifecycle;
+using ClaudeDo.Worker.Tests.Services;
+
+namespace ClaudeDo.Worker.Tests.Lifecycle;
+
+public class RunningOperationRegistryTests
+{
+    [Fact]
+    public void Begin_AddsEntry_DisposeRemovesIt_AndIsIdempotent()
+    {
+        var ops = new RunningOperationRegistry();
+
+        var scope = ops.Begin(OperationKinds.Merging, "title", taskId: "t1", taskNumber: 7);
+        var op = Assert.Single(ops.Snapshot());
+        Assert.Equal(OperationKinds.Merging, op.Kind);
+        Assert.Equal("t1", op.TaskId);
+        Assert.Equal(7, op.TaskNumber);
+
+        scope.Dispose();
+        scope.Dispose();
+        Assert.Empty(ops.Snapshot());
+    }
+
+    [Fact]
+    public void Entry_IsRemovedWhenTheOperationThrows()
+    {
+        var ops = new RunningOperationRegistry();
+
+        Action act = () =>
+        {
+            using var _ = ops.Begin(OperationKinds.Rebasing, "title", taskId: "t1");
+            Assert.Single(ops.Snapshot());
+            throw new InvalidOperationException("boom");
+        };
+        Assert.Throws<InvalidOperationException>(act);
+
+        Assert.Empty(ops.Snapshot());
+    }
+
+    [Fact]
+    public void BeginAndDispose_BroadcastStartedAndEnded()
+    {
+        var hub = new MergeRecordingHubContext();
+        var ops = new RunningOperationRegistry(new HubBroadcaster(hub));
+
+        var scope = ops.Begin(OperationKinds.CreatingWorktree, "title", taskId: "t1");
+        var id = ops.Snapshot().Single().Id;
+        scope.Dispose();
+
+        Assert.Collection(hub.Proxy.Calls,
+            c => { Assert.Equal("OperationStarted", c.Method); Assert.Equal(id, ((RunningOperationDto)c.Args[0]!).Id); },
+            c => { Assert.Equal("OperationEnded", c.Method); Assert.Equal(id, c.Args[0]); });
+    }
+}