Interestingly, you are not even considering the possibility that Messi himself could be the problem
I have not heard about any problems between Mbappe and Neymar, although in fact these are the players who claim to become great in the coming years. I don't think it's possible to blame the coach at all - he has responsibility for the whole team and the results, so his decisions should be carried out without scandals.
Neymar only had problems with Cavani who left the club two seasons ago.
Neymar and Mbappe have good time with each other in PSG but Mbappe does no longer feel happy in PSG. In the summer, he really wanted to leave. Some said he does not want to play under the domination of Messi but only Mbappe knows it is true or not.
The fact with real matches is Mbappe still contributed good matches for PSG. He has more contributions for PSG so far in this season, more than Neymar or Messi. I think the injury will give Messi more time to adapt to a new club. I think with his outstanding level, Messi won't get troubles in PSG.
Mbappe is still performing great even though he wants to leave the team as soon as possible. Yeah, he wanted to leave the team in the last transfer window but PSG resisted Real Madrid's offers and the transfer didn't come true. But he will be available as a free agent this January and I guess that Real Madrid will make a contract offer to him and finish the deal this time.
I think that nothing has been decided yet in this case and that all options are still open, from Mbappe staying at PSG, to going to Real but Manchester City is also interested.
The owners of PSG have decided to gamble this season, keep the 3 best footballers of today together, Mbappe, Messi and Neymar, and finally win the ultimate prize - the European Champions League.
After that, they certainly hope that Mbappe will change his mind and stay in Paris.
The problem with this type of gambling is that the ball can fall on the wrong number and you can run out of everything, players, money and trophies.