Despite owning Klopp's squad legacy, but Slot knew better about United rather than ten hag. If you're watching Slot's post interview, then you would see how he was breaking down Ten Hag's pressing. he even exposed United's tactic to the public.
When you see an experienced manager who knows how to study the tactical structure of his opponents before playing against so he can device a means of coming top at the end of the day, you'll definitely not struggle to notice about his professionalism. Arne Slot came to Liverpool and started with by studying the tactical approaches of his predecessor Jurgen Klopp which was why he was able to use the squad at his disposal effectively without even adding a new player in their mix. Like you rightly said, he exposed the weakness of Erik ten Hag's tactics which was why deviced the best tactical approach to get all three points from the game at Old Trafford yesterday and that actually worked perfectly for him.
Liverpool must accept the fact that they have lost a manager of great quality and will certainly understand the void. The manager who was in charge for a long time and after being in charge, he deliberately stepped away from the responsibility of Liverpool, but the new manager who took charge of Liverpool cannot be said to be applying a brand new strategy. In many cases we see the current manager managing the team with the same strategy that the former manager of Liverpool used to manage the players. The former technique has some advantages in managing teams. Most of Liverpool's players are old, Klopp has been training them for a long time, so if the players play with that strategy, it will be easier for them to understand. But the most challenging thing for the current manager this season is to get Liverpool's current team to at least a good position in the Premier League.