There is probably larger implications to the "project" than pushing a ball on a pitch good but I can't really judge those without being privy to the sort of high politics involved beyond the fact Qatar obviously made large strides as a public facing financial actor in France and PSG.
I think sporting wise it is a failure so far and my own beliefs is that it is based on a flawed, corrupt conception anyway. But football cares little about morality as evidenced by the last decades and perhaps the whole history of professional sports.
There was obviously achievements along the way for them. Easy pickings with unlimited money, you could argue. But achievements nonetheless which not every billionaire's toy can have said to achieve in their respective fields even with unparalleled funding.
They took over a club which had some pedigree and mediatic presence, but an history of inconsistent results and regular internal strife. Admittedly, one that always was somewhat "plastic" since its creation as Paris Saint-Germain (that's Paris for you). Out of that they maxed the club to the full potential and forcibly entered into the current "top teams" club discussion through financial power.
Since in full control they always played the CL and got out of the group stage : 4 quarters, 1 semi and 1 final and 5 times the round of 16 though the latter has become more common since 2016 and marks a regression. There's clearly been a pre & post Neymar/Mbappé era in shaping the team. While perhaps incidental, the first core ultimately blossomed into a more balanced competitive squad even if they hit their ceiling in quarterfinals. Since deciding they wanted to have the two biggest stars possible up top, the quality degraded and shattered the illusion QSI was slowly working towards a more cohesive direction.
One of biggest failures sport-side is failing to implement a real project and stick to it beyond throwing funny money at it. They're burning through coaches and players. The direction has always been far too enamored in getting big names that were way past it (Beckham, Buffon, Ramos perhaps Messi even)... Perhaps in a misguided attempt to correct leadership problems, moreso probably because they crave the publicity.
I don't see any sign of improvement on that front and it will only happen if QSI decide to tighten up funds and be faced with the issue of making their spending efficient. Nasser and QSI are mercurial, way too involved in the public facing operation and bad bosses overall. Internal discipline and professionalism are supposedly way too lax, with the direction encouraging it implicitly or explicitly by showering extensions and wage increases liberally. Wage structure is wack and it would take several years to fix this and the cargo size deadwood they accumulated in the toybox. City, as a direct point of comparison, committed to a project headed by Pep and they did build what is the best team around.
Someone said they squandered the homegrown players (Paris has a massive pool of talent to draw from) and I agree. It's always been a popular talking point way before QSI got in (see the massive Anelka flop that was supposed to be a shift to Paris-born stars) to rely more on it and never truly came to pass except as a cost cutting measure. QSI continues to sell them away and eventually buys some Paris-region born fellas at high prices whenever it's flavor of the day at the board or they're pissed at the foreign stars not cutting it.
They did raise the profile of the academy though, you find a fair few players in current top clubs and the NT. They make a better job selling them too, probably the only bit of sensible business on the recruitment side.
They also paid for a new, state of the art training center. I'm sure it's tied to some real estate dealings on the side but at least that's a net gain for the club, irrespective of owners.
Eventually, and that's my biggest concern, I don't see how it doesn't end up (and it will have to someday) in tears. They could win a CL or two, even for as poor as management is. They almost did already with a not-so-well constructed team. Arguably the club could be in a better position than when they took over the dreadful Colony Capital years after QSI leaves. But I expect there will be a lot of mess too. They made a couple of tangible improvements... But sports side it's all been build on sand and wholly unsustainable without the money hack.