Добавьте файлы проекта.

Updater/Core/ProcessManager.cs

@@ -0,0 +1,30 @@
+using System.Diagnostics;
+
+namespace Updater.Core;
+
+public sealed class ProcessManager : IProcessManager
+{
+    private readonly ILogger _log;
+    public ProcessManager(ILogger log) => _log = log;
+
+    public void StartApp(string installPath, string appExe, int delayMs)
+    {
+        var appPath = Path.Combine(installPath, appExe);
+        if (!File.Exists(appPath))
+            throw new FileNotFoundException("Executable not found after install", appPath);
+
+        if (delayMs > 0)
+        {
+            _log.Info($"Waiting {delayMs} ms before restart...");
+            Thread.Sleep(delayMs);
+        }
+
+        _log.Info($"Starting '{appExe}'...");
+        Process.Start(new ProcessStartInfo
+        {
+            FileName = appPath,
+            UseShellExecute = true,
+            WorkingDirectory = installPath
+        });
+    }
+}