I don't think La Liga are protecting Real Madrid and Barcelona - just look at how Barcelona were screaming 'Unfair !' when they had to release Messi to fall in line with the new La Liga regulations. Reading this
How LaLiga economic controls go beyond Financial Fair Play | Global Fútbol
it srikes me that they are trying to instill some financial responsibility into the system. Their complaint in this instance re Mbappe is against the power of what they call 'State run' clubs (here Qatar). It seems to me they want UEFA to put in similar regulations across Europe to those they have imposed to try and establish a more level (yes, I know, its too late) playing field.
As for 'State run' clubs and the financial advantage this gives them, bear in mind we have more than one (Newcastle, Citeh) in our own League...