Carrick definitely changed the whole United situation, there is no doubt about that. But that doesn't mean that he will continue to do so. He did not had a full season yet, he had a half a season and he did alright during that season.
Because of that, people have some hope that he will do a lot better when given a full season. But that doesn't always happen that way, a simple example that we can all see right now, Arne Slot won the league title on his first year, but failed miserably on his second year. We have no idea if Carrick will be like that or not.
You are right, because he performed well half a season, doesn't mean he will do the same for a complete season, we just have to watch and see.
Bringing Arne slot into this matter is not relevant, he won the Premier league in his first season with Liverpool, because he had the best players he needed. Coming into next season, he let 3 of his key players go ( Luiz Diaz, Trent, and Nunez), after these players left, I haven't seen any good replacement for them, that was why he failed last season. Looking at Arne Slot case, he led himself to his own downfall, we should not just think all managers are like that. Carrick has been in United for years, so it will be expected of him to deliver a good job next season.