Arne Slot is definitely lucky to win it on his first year. Like mentioned, he didn't collected all that much points but everyone else was bad this year. Arsenal once again came in second and that is very normal for them at this point, and I ma not even shocked about it.
But, the fact that City did as bad as they did this season was unexpected. They won four in a year, and that team crumbled to dust this season and nobody expected that and we assume that Arne Slot is great but we are going to see how he is going to do next season. If we can see that then we are not going to judge him any different, then if Arne does great next season it would mean he is great, but if this was just one time thing then that is not going to be great for them that they ended up with just one season title.
You don't also mention Slot's main factor to help him in winning the league is Klopp's legacy. I don't think he could do that without having a full arranged squad as Klopp's legacy. He coached a club that has connection, chemistry, and team work. It makes his burden became smaller, than any other new coach who have terrible squad to start.
That's they reason i think he get some lucks this season, but can't deny the fact if he's doing bad, his club also doing it tho. He deserves a lot of applause, though he came from low tier league.
That is also 100% true, Klopp left a team that was already doing very well together, like even just last year, they won 82 points, which is what they have right now and makes them champions, so what Arne lifted the trophy with is what Klopp became third place. So Klopp already left a team that could do 80+ points to Arne, and that is a big deal as well.
It is still quite important to realize you are not going to see him adding much at all. What we are seeing right now is not that much of a huge deal and shouldn't be considering it as a horrible thing that he achieved neither. He still ended up getting some points and that doesn't mean he did nothing neither, he is still doing a good job and won the league and that is the important part and shouldn't be worrying Liverpool, they should be still sort of happy.