I agree that it is going to take a while for them to get better, it will not be too simple and it will take a while. Winning UCL is a very difficult task, while some teams may win it when you do not even expect it, some teams like City who dominate a tough league like premier league could have hard time getting even just one. This is why I think it is not easy for PSG to win it, but when you least expect it then they may win it too, you never know.
I believe that this season isn't it though, they lost Mbappe just recently, it will take time for them to adjust playing without him, and it is going to be hard for them to get this new team to win something major. If you ask me, even ligue one is in danger right now as well.
Everything will not be easy when they are in the Champions League, they must have everything they need to become champions. Not only in the game, things like mentality and others will still have a big influence on whether they can get something good or not. Many clubs have experienced failure and it's not just them, it shows how difficult it is for a club to compete for the title in the Champions League.
You give a great example when you say Manchester City. In the last few seasons, Manchester City has dominated the Premier League so much that we know it is not easy to dominate there, and even competing is not easy. However, in the Champions League they actually had more difficulties and only succeeded in one of their several attempts to win the title. We can compare the level of competition between these two leagues and we will find the answer. So everything will not be easy for them to do even though they really dominate the league.