Let's say that Pep Guardiola has an easier job than other coaches, but he won't get every player. I doubt that if Mbappe now finally leaves PSG that he will end up playing for Manchester City. At the same time I am pretty sure that Manchester City would try their luck and reach out to him and make at least an offer or have conversations or pre-negotiations or something. But Real Madrid is still the strongest competitor for Manchester City when it comes to signing the best players in the world. Even Haaland recently emphasized that he will not say ever for sure that he will be staying with Manchester City. He said in response to the Real Madrid rumors that he doesn't want to comment them.
But City got Haaland. This is very close to realizing the ability to "get any player" since Haaland and Mbappe will not play on the same team. In fact, City got one of the 2 best strikers in the world, and Real couldn't do it because of the crazy finances that PSG gave Mbappe on a new contract.
As for Mbappe's move to City, this will only be possible if Real buys Haaland.
This is already an unlikely option (since leaks say that Mbappe has already signed a contract with Real), but previously it was quite possible since the compensation for Haaland is comparable to the bonus for Mbappe.