Mbappe is almost certain to leave Paris Saint Germain at the end of the season. This is also his statement. He said he won't stay at Paris Saint Germain even if they win the Champions League. He will probably go to Real Madrid. And because he is going to Real Madrid, if Paris Saint Germain transfers Lamine Yamal, Barcelona will be weaker and Real Madrid will be stronger. If such a transfer process happens, I think Real Madrid will be champions more easily next season.
As far as I know, many of the penalties and restrictions that Barcelona currently has in transfer matters will be lifted this summer. Barca is still heavily in debt but they will at least be allowed to spend as much as they have sold and if Yamal then moves to PSG they will certainly be able to buy several good players with that money. So Real will not be the only one making transfers.
For Lamine Yamal, I don't think Barcelona will ever accept to let go of the young Spanish sensation so I don't think the rumour concerning a possible move to Paris Saint Germaine in the summer is going to materialize
Without having to pay any transfer fees, many teams want to own Mbappé. However, Real Madrid is still said to be the 2018 World Cup winner's top priority. But I think he must take a "huge" salary cut to ensure this deal happens. In 2021, Real Madrid almost welcomed Mbappé in a similar way. At that time, Mbappé reached the end of his contract with PSG and could negotiate with the Bernabeu team. But the deal broke down at the last minute when Mbappé suddenly extended his contract. This time, the same story is still likely to happen. However, that possibility is not high. Kylian Mbappé will definitely leave, and there is no way he will "turn his back" on Real Madrid again.
As for Barcelona, I don't believe they would sell Lamine Yamal and go shopping for another player. They should avoid making the same mistake as in the story of selling Neymar to PSG.