Conceptually, the idea of financial fair play originates from Leeds, Southampton, Sunderland etc, preventing overspending through debt or an owner burdening the club with unmanageable salaries and then essentially walking away and letting the club collapse. I think this is a point that is not often discussed as the rules predates city, but many fans believe the rules were put in place to maintain the hegemony of the 'legacy' clubs.
The next layer which City are challenging was more explicit rules to prevent nation states essentially buying the competition through funneling money through controlled entities. Technically the existing rules should have prevented that, but I guess they weren't explicit enough
Ultimately if Abu Dhabi decided to stop supporting City, once the sponsorships ended they would reset to maybe half what Liverpool United and Arsenal get since their viewership is mediocre. They'd very quickly be bust or have to firesale. I'd be surprised if they could generate the same income as Spurs or Villa (excluding success revenues).
If they are successful, expect Aramco on NUFC's shirt and the largest sponsorship deal in football history. A billion quid is pocket change for them and Saudi, as they claimed with PIF (which is the sovereign wealth fund, and controls the majority of football clubs and the league in Saudi, as well as being the owner of Aramco, and changed NUFC's away kits to green) will claim that Aramco is independently run and not controlled by the state (which extracts 70 odd percent of their profits) etc etc. All meaningful competition in the league will be over.
I'm not super confident about the result though. Money talks after all and ultimately I suspect government influence will result in a settlement and a slap on the wrist. God knows how long the Conservatives sucked on the Russian teat and looked the other way.