Real Madrid is relaxing because Mbappe has shown interest in moving to the club. But PSG is not willing to let him go just like that. The French team will sell him to the highest bidder and make a profit from the transaction. If Mbappe is not sold this in this transfer window, PSG will bear the consequences because he will leave freely next season. I expect Real Madrid to come up with a good offer that can make PSG let him go.
After defending PSG for so long, in the end Mbappe could not resist creating conflict with his own team. Instead of agreeing and being nice to a team that pays him a high salary, instead he loudly wants to go to another team without benefiting his own team. It was something that could be considered treason, but it happens a lot in football where prestige and money are involved.
PSG clearly wants to keep Kylian Mbappe, but cannot force players who want to leave because of a greater desire. Real Madrid are a team that Mbappe is known to be interested in, he wants to play for them and win something that is his ambition. There's nothing wrong with being ambitious, but not in this less fun way.