Everything is alternative theories until it's backed up with evidence, and at this point everyone is speculating.
You chose the side of the argument that suits your rethoric, which is fine, but you say yourself that PSG tried to tie him down for a long time. Wouldn't it be fair to say that they probably threw at him all the money they could throw last year?
So if he did change his mind, what changed? Nobody knows. It's pretty hard to imagine that PSG tried to renew Mbappé for 3 years now and that they kept a secret stash just in case to change the offer 1 week before he leaves for Real Madrid, it wouldn't make a lot of sense, especially since Mbappé could have signed there since january and it would have been too late for PSG.
What we do know though, is that several media and Mbappé himself reported that something had changed in the negociation. He mentionned "i'm thinking because there's new elements, many things, new parameters and I don't want to make the wrong choice". So what was he talking about? Nobody knows, is it about Real's project? PSG's? Money? Another club (Liverpool?) involved? Nobody knows.
I do think it's pretty unlikely that PSG just woke up 1 week before his decision and said "oh Kylian, we've been trying to extend your contract for years now but guess what, we just found money we didn't know whe had!".