If it's a steam catapult, it occupies quite a bit of room and it's not worthwhile/efficient to put it on medium size (<70,000 tons) aircraft carrier. They have the reason to go for EMALS...
Have you count on how many aircrafts they can carry? In addition, what are they?? And what are the usages...
For British, they have F35B backup in the lineup...
For French's Charles de Gaulle, it's nuclear powered... Although they are thinking going back to regular power, which is not in their original proposal...
For Brazil, they are just... fooling around near the coast...
One of the very important issue of having catapult is to launch fixed wing AEW aircraft... Why do they choose fixed wing? One is, they can stay in the air for "LONG", second, they can carry heavier load....
No idea if China will put the nuclear core on the aircraft carrier... It very well depends on conditions... You can tell why Russia has so many nuclear powered submarine but they don't even have one nuclear aircraft carrier in deployment... From French's case, you know how dangerous it is to put a nuclear core on an aircraft carrier...
Yes, there is a trend. Smaller remote planes can do some works, but not all... And, it doesn't relate to why US scale down the size of the big aircraft carrier... Otherwise they will think of building medium size aircraft carrier.
I think what you have missed is the term "efficient"...
For China, for sure, they will try putting the nuclear core on the ships, but it will be difficult because of the confined space and maintenance... It may not be as wise as using conventional power...