We never know, they haven't even decided who will be the new coach. however, rumors of Galtier's dismissal have been circulating and have been confirmed by Fabrizio Romano. I'm pretty sure if Mbappe will stay with PSG, at least we'll still see him wearing a PSG shirt next season. now, Nagelsmann is the strongest candidate as their new coach. it is even reported that there has been no contract agreement with PSG, but his agent is already in Paris to have a serious meeting with the club.
If in the end there is a deal, I'm pretty sure if he can bring PSG much better than Galtier. but there is one problem, can Nagelsmann have full control in the dressing room. if so, I am optimistic that PSG will be able to bounce back. regarding players, they can bring in anyone after all PSG has abundant finances. The problem is, so far no coach has been able to bring PSG to lift the Champions League trophy. maybe with Nagelsmann and a series of new players brought in, PSG's lucky season will come. but by the way, this is just a personal opinion, even the league competition just ended. so, we'll see how it turns out later.
Nagelsmann will most probably be their next manager and that has a good side and a bad side. The good side is that he is a manager who finds the amazing talent in places nobody looks, with some of their big names are gone (and excepting to see Neymar leave too) I would guess that a manager like Nagelsmann who will build a great team could actually be the thing they are looking for, he will be perfect fit for them in the first 3 months or so.
However, he is not a tactical genius which means that he is not going to be all that great after like 6 months, when all the transfers are done and its the dog days of the year, he is not going to be able to adjust his system to whatever team needs and that's when they will realize it wasn't a great idea. He is the anti-ancelotti, ancelotti takes a team that's ready to its peak ever possible unlike anyone else, but doesn't usually build it himself.
In fact, football fans are really waiting to see which season the main objective of PSG team will be fulfilled. That is, PSG's main objective is to secure the Champions League title, which the team has repeatedly failed to do every season. Looking forward to seeing how the team shapes up in the offseason.