Even though PSG has not won the UEFA Champions League trophy, they are a team to be afraid of when playing against in the UEFA Champions League. In the modern-day UEFA Champions League, it is only Real Madrid that has won the UEFA Champions League back-to-back, so it will be a little bit hard for Manchester City to follow Real Madrid's full steps.
Who scared with PSG lol, it just the fans that think they're strong because they can dominate in Ligue 1. PSG isn't a strong club, yeah they can beat Aston Villa, Dortmund, Roma, or any other mediocre clubs in top domestic leagues, but it's not enough to beat Bayern Munich, Inter, Real Madrid and Manchester City.
Imagine if Mbappe leaving PSG, I think people will stop favoring PSG in International league.
It is very likely that this will happen and not only that, but Ligue 1 will also very likely lose a lot of viewers broadcast internationally because one of its attractions is no longer in the league and PSG will also lose a lot of income from merchandise sales because PSG became even more famous when Kylian Mbappe played there.
In the Champions League, we can be sure that PSG will always get a spot every season because in the league they will still be the strongest, but their presence in the Champions League will be counted as an average team which might cause surprises but will not always get a place as the favorite team.
With the financial power that the club has, it is still possible for PSG to turn this team into a stronger one in europe competitions even without Mbappe's presence, but that will take a long time because no success can be achieved instantly.