It seems Khvicha Kvaratskhelia is not going to leave Napoli. He was about to join Real Madrid in the first but they didn't send him any offer and then he was about to join Barcelona but they didn't have enough money to hire Khvicha Kvaratskhelia and then he would leave Napoli anyway that's why he started negotiations with PSG while we were still under contract with Napoli.
Now his agent said he is not going to leave anymore and Khvicha Kvaratskhelia will stay in Napoli and play there in the next season since Conte wants to have him in the team.
Weeks ago, before Euro 2024, I read news that Kvaratskhelia was convinced by Conte and his project for a new season. The impressive performance in Euro 2024 with his national team helped his name to be known and wanted more. He can decide to stay with Napoli if he loves this club and wants to contribute more for them.
I see chance for Kvaratskhelia to succeed more with Napoli is very small and it's better for Kvaratskhelia if he leaves Napoli and join a bigger club even outside Italy. In Italy, I think a most promising destination for him is Inter Milan which managed to play well in Champions League recent seasons.