Don't act as if PSG has no idea what to do, they knew that it was possible for Mbappe to leave all the way last summer when he rejected making another deal, and they knew it since February when he basically declined the official offer as well, and everyone started to talk about how he is going to Real Madrid. So they probably worked on what to do since then, and we are going to see how it will unfold.
Several people know that Mbappe will leave PSG this season after Mbappe did not want to extend his contract. But I'm sure the club management would have known beforehand and perhaps they would have had private discussions with Mbappe's agent. There's no way they didn't anticipate this. I think PSG is already looking for several new strikers and we only know the names of several famous strikers who also happen to be among PSG's targets. Some time ago, many media reported that PSG was trying to negotiate with Kvaratskhelia and Osimhen. But lately I have also seen rumors on Twitter saying that PSG is targeting Rashford or Lamine Yamal. We don't know who Mbappe's replacement will be next season but I'm sure PSG will get him. They have money that makes everything possible.

As much as we know the news about PSG and Mbap as much as they have reported but there are many things beyond our knowledge that are hidden between the management and Mbappe. PSG team management already knew that Mbappe would not stay at their club although they did not spare any effort to keep him but still they could not keep Mbappe in the end. Since Mbappe is certain to leave, they should have already targeted which player they will sign next when Mbappe leaves their club. PSG could have completed the contract with the player if they had discussed with the star in advance. But now it remains to be seen which star player will be signed by this SG in the end.