The financial situation of PSG is what makes them different from other clubs of Ligue 1. The difference is honestly too much, even more than Bundesliga. Bayern has dominated the Bundesliga for a long period of time, but the competition gap has not been this much. I don't think Mbappe's leave would stop them from winning the league, but it would definitely be tougher to win it.
Indeed, they have no problem with their financial situation. They also have well-managed management. And they also still have many chances to get more talented players again, although it may not be as super star as Mbappe right now.
In the French league and other local leagues, PSG will not experience significant changes, especially in first place in the French League. Even without Mbappe, PSG, I'm sure, will still be the title holders. Because so far, there is no other club that can compete with PSG with high consistency and solidity.
However, it might be a little different when they leave the league in France. Like at UCL of course. Without Mbappe, it might be a little difficult for PSG to win or at least get to the UCL final. Moreover, if they don't or haven't found a suitable player to replace Mbappe, this will be quite difficult. Unless they can find a replacement for Mbappe whose performance is at least not too far from him, this will probably be quite difficult. However, they shouldn't only focus on 1 player because PSG also has to strengthen their midfield and rear to become a club that is truly strong from all sides.