The option to extend the contract for a year depends on Mbappe and he has not activated it. PSG can literally do nothing in this situation. Mbappe will leave for free in the summer and I don’t see what can be discussed here. Taking into account the fact that he returned the loyalty bonus to PSG (a gesture of goodwill), it can be assumed that the parties reached a peace agreement and Mbappe will simply finish this season and leave.
In my opinion I think for Mbappé to remain at PSG next summer depends on their performance in the Champions League and even if they win the league trophy it won't be enough to keep him in the team, lets not be quick to forget that he almost forced himself out of the his current team, and even had a secret contract negotiation with Realmadrid, which made PSG to increase his release clause and I was surprised to see him sign another 1 year contract with them.
But in the new contract he signed, Mbappé is free to negotiate with any team of his choice after this season but PSG would sell him for the right price though they would still try as much as possible to keep him but like I said earlier, their performance in the Champions League determines whether Mbappé would remain in the team or not, else I think he could move to Realmadrid by summer.