feat(worker): session skills SignalR surface + per-level persistence

tests/ClaudeDo.Worker.Tests/Repositories/AppSettingsRepositoryTests.cs

@@ -72,6 +72,43 @@ public class AppSettingsRepositoryTests : IDisposable
         Assert.Null(row.CentralWorktreeRoot);
     }
 
+    [Fact]
+    public async Task UpdateAsync_Persists_SessionSkills_Json()
+    {
+        using (var ctx = _db.CreateContext())
+        {
+            var repo = new AppSettingsRepository(ctx);
+            await repo.UpdateAsync(new AppSettingsEntity
+            {
+                SessionSkills = "[\"ponytail\",\"ponytail-help\"]",
+            });
+        }
+
+        using var readCtx = _db.CreateContext();
+        var row = await new AppSettingsRepository(readCtx).GetAsync();
+        Assert.Equal("[\"ponytail\",\"ponytail-help\"]", row.SessionSkills);
+    }
+
+    [Fact]
+    public async Task UpdateAsync_Blank_SessionSkills_Stored_As_Null()
+    {
+        using (var ctx = _db.CreateContext())
+        {
+            var repo = new AppSettingsRepository(ctx);
+            await repo.UpdateAsync(new AppSettingsEntity { SessionSkills = "[\"a\"]" });
+        }
+
+        using (var ctx = _db.CreateContext())
+        {
+            var repo = new AppSettingsRepository(ctx);
+            await repo.UpdateAsync(new AppSettingsEntity { SessionSkills = null });
+        }
+
+        using var readCtx = _db.CreateContext();
+        var row = await new AppSettingsRepository(readCtx).GetAsync();
+        Assert.Null(row.SessionSkills);
+    }
+
     [Fact]
     public async Task DailyPrepMaxTasks_defaults_to_5_and_persists()
     {