You are correct. They will not leave psg before 2022 world cup. I do feel though that Qatar have used psg solely as a political bargaining tool.
Don't think the club has to complain.
We went from being under the very worst owner of our history that almost managed to make us going down in Ligue 2, which has never happened in our history, to being successful in the league, the national cups (well we were already specialist in that matter) and being relevant in Europe again (after our 5 consecutive european semi finals in the 90's ).
Sure, the fanbase is less good in the stadium than utiliser was 10 years ago but it has to do with the events that unfolded before the Qatar takeover (battle between rival fans of PSG, deaths, etc.).
The club will get a state of the art academy that pretty much no one can dream to build in France (and few in the world), they upgraded the stadium while it remains a property of Paris city, they pay a shit ton of taxes that benefit french people.
And the joy to see players of that quality is simply a gift. Some of them are straight up among some of our best players ever under our shirt like Zlatan, Neymar (Ronaldinho was good but didn't show enough at PSG during his time). Even the fans of our opponents hate us but like to see those players against their team in real life.
Sure, they are often doing a mess with the sporting director position but overall, they did a pretty solid job.
They took a club for 80 M and made it one of the biggest brands in the world while playing in a less exposed league and considered the hypest club in the world thanks to their collaboration with Jordan and co.
It is way better than what i had initially imagined. And we will be well off when they will decide hey have done enough.
And to be fair, they gueninely want to win the Champions League and back up their ambitions (Neymar, Mbappé). An owner that only care about winning, isn't that what any fan dream about ?