Mbappe has not signed a new deal with PSG. His current contract will expire in July of next year and he'll be a free agent. PSG is still looking for ways to make him renew but I doubt it would happen even though I don't put anything past Kylian Mbappe. He may decide to renew.
If I'm not mistaken I understand that in this transfer window PSG extended Mbappe's contract until 2025. In the first situation, Mbappe did not agree with the club to extend the duration of the argument, but later when he was given pressure from the club that either he had to leave the club this season or he had to extend the contract with PSG, in that situation, Mbappe extended the contract until 2025. Mbappe considered leaving PSG as a free agent member but if he left the club as a free agent member, PSG would have faced a huge financial loss, so PSG pressured Mbappe to extend his contract to avoid that financial loss. If Mbappé moves to a club while his contract is still in place, the club will certainly receive the transfer fee he leaves.