For Mbappe, the best action to take would be joining Real Madrid this summer and it seems like he will. Real Madrid are his dream team and Real Madrid want to sign him so bad too. PSG wouldn't be able to do anything to keep him for at least one more season I think. Whether they win the Champions League title this season or not, Mbappe wouldn't care about it and still would join Real Madrid. And considering his future, I think that it is better than staying at an unpredictable team like PSG. Real Madrid are a far more promising team than them.
If it was some smaller club then I would guess that "his childhood dream team" would not matter at all. If his childhood dream team was like Lille or something then we wouldn't see him leave for that club, or at least not for another 10+ years because Lille wouldn't be able to pay him near what he is getting right now.
The difference is that Real could pay him amounts that he could not get in most other places, there are only a handful of clubs that could even get close to paying for something like this and they are not going to be a lot of teams so Real was one of those teams and they had the money ready for it as well since they knew there was a chance of this happening.