I agree with you, and to achieve that, it is very difficult, there are teams that are very good that find it difficult to achieve that, because most of them or they do well in their leagues and badly in the UCL, or they do badly in the leagues but very well in the UCL, Madrid has been a clear example of such a thing, however we as fans know very well that Liverpool comes from very good team organization with KLOPP, so the new coach only works on that scheme and from there on he has been able to do things well, it is difficult to change everything from one moment to another, it is not that easy, in this case they are doing things very well and I like it.
If you look at Liverpool's games for the next 3 to 4 weeks, you can see that they have a match every 3 days and will play against very strong teams like Chelsea, Arsenal, Leipzig or Leverkusen. It's going to be a very tough few weeks for the players and now it will really show whether the new coach has what it takes to replace Jürgen Klopp or whether it's too much for him and the team.
Although Klopp managed to make Liverpool have a good squad, that does not mean it will make Arne Slot's job easier as Liverpool's new manager. Because anyway, if for example Arne Slot does not have quality, then it is certain that Arne Slot will fail at this moment. But, because Arne Slot has good quality, it makes Arne Slot able to keep Liverpool good so far this season. So, when Klopp has left then it no longer has anything to do with the Arne Slot era because of course, as a manager will always have his own way to build a team, not only to continue Liverpool's previous success with Klopp.
About Liverpool's future schedule I think it is clear, Liverpool will get a busy schedule and with difficult opponents and of course this will be a real challenge for Arne Slot to show his quality as a manager worthy of Liverpool.