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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.
Mbappé will probably be in the first 11 in the match against Atalanta tomorrow. Ancelotti sees him as one of the team's important stars. And this is normal because he is one of the best players in the world right now. Considering that he will definitely play in the first 11 at Real Madrid, I think he has made a logical decision. He has already contributed a lot to Paris Saint-Germain with his individual talents, but he has not received the individual awards he deserves. I think he will also receive individual awards while playing with Real Madrid.