It seems like Ancelotti is quite capable of managing Madrid dressing room in harmony, so Perez doesn't have to step in to make a statement that no player is bigger than the club. Mbappe definitely understands the situation well, he has to suppress his ego if he wants to be treated well by other players.
Meanwhile, Ancelotti has proven to be adept at rotating his players, where each Madrid player will get a role according to their abilities. With the many competitions that Los Blancos will participate in next season, I think all players will get a fair opportunity to show their abilities.
On the other hand, Mbappe certainly needs to adapt to the new squad, and I don't think he will need long. If the process goes according to expectations, it would not be surprising if next season Mbappe will become La Liga top scorer. With the addition of Mbappe, Madrid should be able to defend the Champions League and La Liga trophies next season.
Florentino Perez made the statement that no player is bigger than the club when Real Madrid missed out in signing Kylian Mbappé two years ago. He also made the statement when Ronaldo left the club that Real Madrid is not missing the Portuguese superstar. For me, I think he needs to restate this fact because Mbappe has some behavioral flaws. He is a player who wants all the money and attention. Mbappe wants to be the highest goal scorer and this makes him to be selfless.
I agree that coach Carlo Ancelotti is experienced and can control any player. His age and accomplishments are enough for him to command respect in the dressing room. Real Madrid didn't pay much for the Frenchman so they will be willing to take disciplinary actions against Mbappe anytime he misbehaves. Selection will indeed be a problem but Mbappe's position is uncontestable because the striker is in top form.
If Ancelotti can control the dressing room and the players play with a common goal without competition and selfishness, Real Madrid might be unstoppable next season. They have the best management, coach, and players.