The transfer will happen sooner or later, because from the information gathered he has already reached an agreement with PSG and his salary will be 4 or 5 times his current salary at Napoli. PSG is not a team that can polish any player, they always buy ready made players for exorbitant fees, PSG and Manchester City are the reason why transfer market of today is like this, buying players with big money. Besides PSG didn't sell Mbappe for a penny, he Mbappe was a free agent and Real Madrid got him for free.
That is a very natural thing and I think it is not a complicated problem as long as teams like PSG and Manchester City can afford it, because a team must have a higher financial level in order to recruit ready-to-use players and can improve the quality of their game in every match. And for now PSG does need to target players with that model because PSG still often fails when competing in the UCL so it is quite natural for PSG to buy players who no longer need to be polished perfectly for such a long time.
In this case PSG seems to be in good financial condition, so they will not be in trouble when bringing in another star player with high prices and salaries at this time, so far we know that their habit of bringing in star players will have an instant impact on their performance but will it improve their mentality in the UCL, of course we don't know yet?
From what was reported by Fabrizio Romano about Kvaratskhelia's transfer, it is clearly 99.99% likely to happen and we just need to wait for PSG to introduce it to the public, honestly at this time I see that bringing in Kvaratskhelia is a smart transfer strategy before they will also recruit osimhen later, because previously in the summer, PSG had wanted to buy osimhen and Kvaratskhelia as a package but was rejected by Napoli.