We have to believe that Mbappe extended his contract with PSG because a club like PSG would never let Mbappe leave the club as a free agent. A player of Mbappe's stature, with a club planning a maximum transfer fee, would never expect PSG to release him as a free agent.
You see the possibility of Mbappe leaving the club next season but I don't, in the previous several seasons we have seen Mbappe not leave the club even though he made the possibility of leaving the club. The next transfer window may see him leave the club again but ultimately he will remain at PSG again.
As long as Mbappe sees money bigger than his career, he will not be able to leave and go to a better club.
If so, that means Mbappe doesn't have any chance of collecting trophies. If you look at how PSG is treated at UCL, his thirst makes Mbappe more aware that staying at the club is not just about money but must be able to consider his career and future in the world of football. Staying at PSG is not a good option at all. In fact, his name will not be on the list of top players who won the Ballon d'Or. The situation at PSG is very complicated, so Mbappee needs to gain experience at a club like Madrid because that is the only option that can be taken instead of staying at PSG. No matter how PSG holds him, the decision is still up to Mbappe. His contract will end soon and it would be better to leave a club that doesn't look like it has the potential to win the UCL trophy.
Kylian Mbappe is believed to have reached agreement with Real Madrid to join the Spanish giants next summer but what Paris Saint Germaine management never wanted to accept was to watch the Frenchman leave the Parc des Princes for free and that's why they wanted a year contract extension with the club so that Real Madrid would pay good sum of money when they sign Mbappe next summer.
PSG has a major role to play in terms of deciding the player's future but can't totally stop him from leaving the club if he wants to and that's why the want him to leave when the club will stand to gain meaningfully from his departure.