You are basically right about this that Mbappe becomes cheaper as a free agent under normal circumstances, but nothing is normal when it is about Mbappe. He now wants the money that he would have earned from playing for PSG next season to be put on top of whatever he receives for a transfer from PSG to another club this season. Either the sheikhs are willing to pay him some form of compensation or the new club has to put the money on top. In poker you call that Mbappe move "ALL-IN". he isn't making a step back, he wants it all and I hope that even he has to realize at some point that enough is enough but my expectation is that he will get whatever he wants.
In all of this I think the people that have something to lose is PSG.
If they sell him this summer, then they lose their best player, if they keep him for one more season then they lose their best player, but worst, for free.
Both Madrid and Mbappe can wait one more season. I think it will actually benefit Madrid and Mbappe more if they wait one more season.
PSG is not a club that does good football business or else they wouldn't have been losing much from this. They should have sold Mbappe when Madrid were wiling to pay 150 million or thereabout for him. With money like that you can get a perfect left winger and center forward. It's still not to late for PSG to make good business out of this situation. If Mbappe is staying for one more season, that gives them enough time to scout for replacements. If he's going to leave this summer, they can get money to get a replacement this summer.
Whatever the case, this deal needs to be concluded on time, so both Madrid and PSG will know how they can prepare for the season ahead.