They didn't pay to PSG, but they pay to Mbappe. I think you're very wrong about Madrid's chance to win the title. Mbappe ain't nothing without Madrid. Did Madrid have mbappe last season when they won UCL trophy?
Look at how Madrid won UCL again, and PSG was trophyless last season even when they had Mbappe on their side. We're talking about the fact. It's delusional to think Madrid could win consecutive titles without Mbappe.
We can’t just just accept any information printed on any new outlet, firstly there is definitely going to be bonuses paid to Mbappe by Madrid because we all know that Madrid had to put out some incentives that would have drived him to them by rejecting some of those ridiculous offers from other clubs but can we be certain that it is upto 150M meant for his fees, i doubt that, because I could recall that Madrid didn’t want to break the bank then for such amount to when he was at PSG so they cannot simply pay that, but maybe if he sees his contract to the end this bonuses will amount to that, for now no concrete reports about this.
Also I wouldn’t say Madrid doesn’t need him, they can be more better with him in the team than now. PSG had him last season and weren’t trophyless because they won the league and the domestic cup. Only him been on the team cannot translate to winning trophies but at Madrid he is surrounded by other players who are almost of same quality like him and that will make the team stronger and better