Liverpool will again be a title contender in the Premier League and it is also possible that Liverpool will be stronger in the Champions League next season. But for the FA Cup and the Carabao Cup, it seems that this will not be Liverpool's main focus because if Liverpool focuses on all these competitions to become champions, of course their players will be very tired which can cause the loss of the possibility of becoming champions in bigger competitions such as the Champions League and the Premier League.
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.
It might be different for Klopp, but I don't expect Liverpool to be able to defend the title next season. They were lucky that everything worked out in their favor this past season which enabled them to win the title. Nex season might be different, because many clubs have bought new player and some clubs that were in a poor form last season based on injury will pick form next season.