Well if there is any reason one should place around mbappe move to Real Madrid then it would be the one that his idol actually played in that club, mbappe idolize Ronaldo so much that he is dyeing wish to play in that club is just something else and I believe that's the reason why he left when his contract has expired because his move to Madrid has been far too long being delayed and the speculation around his transfer is that he went as a free agent to Real Madrid.
I think your assumption is that there is no continuity at all, his move to Real Madrid was not because his idol played for the club, but he had other ambitions that were difficult to win at PSG. If given the chance, he would be honored to play on the same team as his idol rather than playing for a club where his idol once played. Real Madrid is a big club, it has achieved various achievements, it is very difficult for any player to refuse an offer from Real Madrid, especially if they are guaranteed to play as a starter. Now he has the chance to win his first title with Real Madrid as they will soon face Atalanta for the European Super Cup.
1,2,3 !HALA MADRID!!!
That's what Mbappe said when he was introduced to the Bernabeu public, the same words with the same expression as his idol Cristiano Ronaldo, so I conclude that he really wants to follow in his idol's footsteps along with his success of course.
However, I agree with you that Ronaldo is not the only reason why he wants to play at Real Madrid, but there are other things he wants to achieve that are not easy to do with his previous team. While at Real Madrid the opportunity is wide open because Real Madrid is a big team with the success they have been able to achieve until now. The big dream of a player is to be able to achieve success with the team or individually. At Real Madrid, apart from the success with the team that he can get, individual success is also a big opportunity because Real Madrid has players who support each other.