I think first of all Liverpool will try to defend their Premier League title because that is already quite prestigious. All the cup tournaments will be secondary. And of course the Champions League is always a priority for every team. But as this season showed even though Liverpool were in excellent form they could not compete in the Champions League and dropped out at a fairly early stage. If you look at Liverpools history they rarely manage to maintain good form over several seasons. At least that was the case with Klopp, we will see how Slot handles it.
Liverpool already had good squad which is capable of defending title but as they are strengthening their team it's just going for all way because now with the arrival of few players they can play much better and fearless soccer which will allow them for having better results in all competitions.
First season was tested case for Arne Slot which give him bonus with title now how things will be works it's challenging because Arsenal is already their while Manchester City is also improving their depth which will increase challenges for Liverpool with their consistency is going to be important in coming season while they will be fought for title here in Champions League. In last season, all was already settled through Klopp era now Arne Slot surely need to work on his own way which will give him some competitiveness while they will be in for double.