You’ll always see arguments about states v businesses resident there v funds etc. City argue that they are not owned by the state, Newcastle the same, but there are those who think the ties are too close for comfort (eg although Newcastle is owned by the PIF, most people think MBS de facto controls it so it’s equivalent to state ownership).
The prohibition on owning two clubs, I think, is a Premiership rule, albeit one that might be mirrored in other national leagues, hence Red Bill can own two clubs in different leagues (also City with investments across the globe, including Europe).
It all comes down to sporting integrity - the Premier League won’t accept any half measures (hence also loan players can’t play against their parent clubs, but Spain, for example, allow that). UEFA seem to be more relaxed but I’m pretty sure there was some investigation when the Red Bull clubs played each other to ensure there would be no collusion / match fixing.
EDIT
UEFA ruled that the Red Bull clubs were not under common control so OK to both play in CL. They played each other in the Europa League in 2018.
https://www.bbc.com/sport/football/40348340.amp