dedicated_room: properly initialize logging (#7468)

src/dedicated_room/citra-room.cpp

@@ -152,6 +152,7 @@ static void SaveBanList(const Network::Room::BanList& ban_list, const std::strin
 static void InitializeLogging(const std::string& log_file) {
     Common::Log::Initialize(log_file);
     Common::Log::SetColorConsoleBackendEnabled(true);
+    Common::Log::Start();
 }
 
 /// Application entry point