It's wrong my friend. Real Madrid was not getting him for free. Mbappe left from PSG as a free agent, but Madrid paid 180 million signing bonus to sign him into the squad. In conclusion, Mbappe was not free at all.
I think what you said is also true, because being free on a transfer fee does not mean the player is completely free. Especially considering the salary of a player like Mbappe himself, which is also not a small amount, so we don't have to assume that all of that is free just because of the free transfer fee. In addition, for now Mbappe has to work hard to maintain Real Madrid's strength besides he has to continue to adapt to the players in the Real Madrid squad.