core: Partially persist emulation state across game boots.

src/yuzu/bootmanager.cpp

@@ -120,8 +120,8 @@ void EmuThread::run() {
         }
     }
 
-    // Shutdown the core emulation
-    system.Shutdown();
+    // Shutdown the main emulated process
+    system.ShutdownMainProcess();
 
 #if MICROPROFILE_ENABLED
     MicroProfileOnThreadExit();

src/yuzu/main.cpp

@@ -294,6 +294,7 @@ GMainWindow::GMainWindow(std::unique_ptr<Config> config_, bool has_broken_vulkan
 #ifdef __linux__
     SetupSigInterrupts();
 #endif
+    system->Initialize();
 
     Common::Log::Initialize();
     LoadTranslation();