For me, I think PSG management will not want to allow Mbappe to leave PSG as a free agent after they have spent so much money on Mbappe. PSG management might give Mbappe another lucrative deal that will make him remain at PSG. PSG has built its team around Mbappe, and it will affect PSG's performance next season if they allow Mbappe to join Real Madrid before the start of next season. But let's wait and see what will play out between Mbappe and PSG.
When the duration of his contract has ended, there is no reason for PSG to keep him any longer unless a new agreement is reached between the two parties to continue the new contract agreement. Problems that have occurred between Mbappe and PSG that have not been resolved can be pursued through legal channels, Mbappe can appoint a lawyer to help resolve the problem in court.
PSG has received the consequences of its selfishness in always locking Mbappe away from going to another club, now they have lost a player who has a high selling value for free. In my opinion, Mbappe will stick to his decision and will never extend his contract with PSG.