There is no significant change in Liverpool's game, they are still solid, I agree with you that Liverpool's new coach still has a positive impact and Liverpool's game also still applies the tactics played by Klopp, so I hope they remain consistent with their game until the end of the season to tighten the hunt for the Premier League title this season, regarding Man United for this season they play no changes whatsoever even though there are many new players there, but all of that has no impact on their game pattern and even bad results always befall them.
Klopp started well last season and was hoping Liverpool could do well in either the English Premier League or the Europa League, but the late performances have been underwhelming. It was beyond our expectation that they would suddenly perform so badly at the end. This season Klopp left Liverpool and a new manager took charge of Liverpool but in many tactics we see Liverpool using Klopp's tactics. Klopp has basically been in charge of Liverpool for a long time and every player is familiar with his tactics so it is not possible for a manager to suddenly come in and change the entire strategy of the club. Whoever is currently in charge of Liverpool will be expected to at least perform better this season than last season for Liverpool.
Honestly after he mentioned he will be retiring, the team didn't do that much justice to him neither, between him and Salah arguing openly, and him not getting the results he wants, it was clear that Liverpool just didn't care since he was leaving so there wasn't anything he can do. This resulted with Klopp probably regretting letting it known beforehand, he should have kept that to himself and just let the management know, but I am sure that even in that case he would be probably leaked and use that as selling news and make money.
In the end, we are talking about something that will take a while, if that's the case then we are going to end up with Klopp having a bad season right after that retirement announcement, so Arne Slott doesn't have any arguments about it, he is not retiring and players should try their very best this season. Liverpool looks like one of the best teams in the league and that is why I believe that we are going to see them do fine.