Display: Don't clear display callback listeners when starting a new exec.

Fixes https://github.com/RetroAchievements/RAIntegration/issues/1186

Core/System.cpp

@@ -54,6 +54,7 @@
 #include "Core/HLE/Plugins.h"
 #include "Core/HLE/ReplaceTables.h"
 #include "Core/HLE/sceKernel.h"
+#include "Core/HW/Display.h"
 #include "Core/Config.h"
 #include "Core/Core.h"
 #include "Core/CoreTiming.h"
@@ -409,6 +410,8 @@ static bool CPU_Init(FileLoader *fileLoader, IdentifiedFileType type, std::strin
 
 	CoreTiming::Init();
 
+	DisplayHWInit();
+
 	// Init all the HLE modules
 	HLEInit();
 
@@ -496,6 +499,8 @@ void CPU_Shutdown(bool success) {
 	__KernelShutdown();
 	HLEShutdown();
 
+	DisplayHWShutdown();
+
 	pspFileSystem.Shutdown();
 	mipsr4k.Shutdown();
 	Memory::Shutdown();