I don’t particularly think that without Mbappe, PSG will face hardships. At least not in Ligue 1. Football is not played by 1vs11, rather it's a team game. Yes, it can be argued that Barca became arguably worse after Messi's departure but they weren't really that good when he left.
Losing Mbappe is no different from Barcelona losing Messi before, but the difference is that Barcelona can actually recover more quickly considering that so far Barcelona has prioritized teamwork even though Messi is Barcelona mainstay on the front lines, so losing Mbappe will not make PSG difficult for rise but not as quickly as what happened to Barcelona, because previously PSG tended to be more dependent on Mbappe so far, so like it or not, Enrique has to be able to get rid of that dependence next season so that their can rise again.
If you talk about PSG, they have good finances, a solid coach, and a decent amount of players in the club still. If they play their cards right, they can still dominate the Ligue 1.
Strong finances make it easier for a team to gather star players, but this does not guarantee that they can unite as a team because it has been difficult to unite the egos of star players so far and we have seen this happen at PSG when Messi, mbappe and neymar played together before.
About the UCL, Luis Enrique would need good reinforcements, as they couldn’t win it even with Mbappe. He needs to sign a proper striker and then need to balance out the whole squad, and if they do that, they might do well in the knockouts.
Whether Mbappe is there or not will not be different for PSG so far, they will continue to have difficulty winning the Champions League even though their main squad is filled with star players, unless Enrique succeeds in changing PSG's playing pattern to play more collectively and also improve the mentality they have had so far.