GSRunner: Kick screenshots on the GS thread

Instead of from the "CPU" thread.

pcsx2-gsrunner/Main.cpp

@@ -77,6 +77,9 @@ static std::string s_output_prefix;
 static s32 s_loop_count = 1;
 static std::optional<bool> s_use_window;
 
+// Owned by the GS thread.
+static u32 s_dump_frame_number = 0;
+
 bool GSRunner::SetCriticalFolders()
 {
 	EmuFolders::AppRoot = Path::Canonicalize(Path::GetDirectory(FileSystem::GetProgramPath()));
@@ -286,6 +289,13 @@ void Host::ReleaseHostDisplay(bool clear_state)
 
 bool Host::BeginPresentFrame(bool frame_skip)
 {
+	// when we wrap around, don't race other files
+	GSJoinSnapshotThreads();
+
+	// queue dumping of this frame
+	std::string dump_path(fmt::format("{}_frame{}.png", s_output_prefix, s_dump_frame_number));
+	GSQueueSnapshot(dump_path);
+
 	if (g_host_display->BeginPresent(frame_skip))
 		return true;
 
@@ -657,15 +667,8 @@ int main(int argc, char* argv[])
 
 void Host::CPUThreadVSync()
 {
-	if (!s_output_prefix.empty())
+	// update GS thread copy of frame number
-	{
+	GetMTGS().RunOnGSThread([frame_number = GSDumpReplayer::GetFrameNumber()]() { s_dump_frame_number = frame_number; });
-		// wait for the previous frame to complete (and thus dump)
-		GetMTGS().WaitGS(false, false, false);
-
-		// queue dumping of this frame
-		std::string dump_path(fmt::format("{}_frame{}.png", s_output_prefix, GSDumpReplayer::GetFrameNumber()));
-		GetMTGS().RunOnGSThread([dump_path = std::move(dump_path)]() { GSQueueSnapshot(dump_path); });
-	}
 
 	// process any window messages (but we shouldn't really have any)
 	GSRunner::PumpPlatformMessages();