We must know the main problem, Mbappe wants to stay with PSG for one more season because he has a bonus if playing one more season based on the contract agreement, but he did not want to extend the contract here we can assume that he pursues a bonus. While PSG doesn't want to be like that because next season he can go and PSG doesn't get anything as free transfer so PSG must get a new contract at least until 2025 in this situation, of course PSG is uncomfortable and they can just release mbappe in this transfer window or in the middle of the season what is clear before the contract ended in June 2024.
I don't really know if that bonus that Mbappe would receive is really that big of a problem for Paris Saint Germain. In the end they are owned by a sheikh and everything gets paid by him anyway so that bonus payment should not be that big of a problem. I also don't think that Mbappe's main reason why he wants to stay another year at PSG is that bonus. As far as i know he is earning 72 Million € per season at PSG at the moment which makes him the best paid footballer in Europe by far. So he does not really need that additional money i would guess.
I think that Mbappe will stay another year because his primary target, Real Madrid can not buy him in this summer because they have already bought Bellingham and Real has pretty high debts already. So they need to wait until the end of the coming season to sign Mbappe.