The problem is that the manager they got is not one that is famously known, or ever won any UCL before. Which means that the players may not care about what he has to say. Sure they will act as if they care for a while and if the results come from what he says then they will care even more, but if they do not suddenly become much better team then they won't care about it and they will start to ignore him as well. This is the problem with hiring a manager and saving some money from it. They should have spent as high as possible, because having a great manager is as important as having Mbappe. If you ask me would you rather be me as manager and mbappe on the team, or Zidane as manager without Mbappe, I say zidane would be a better choice.
I don't think the contradictions between Mbappe and Neymar are so serious and it's more of a public game. One of the tasks of the head coach of the team is to build such relationships in the team so that the personal relationships of the players do not interfere with team play and results. By the way, it is not at all necessary that the players have cloudless relationships, on the contrary, internal competition between players is useful to a certain extent, the most important thing is that it does not take ugly forms. For Galtier, the beginning and the first half of the season will be decisive, if there are good results and a team game being built, then there is hope that the players will take the requirements of the head coach seriously. If there is no game, no results, then the intrigues of the star players at the Paris Saint-Germain management level will flourish again with all their might and the main guilty party will be the head coach, as it usually always happens.