China has nuclear-powered submarines, which means China is able to manufacture portable nuclear power-plants.
Then, why is the latest Chinese aircraft carrier Shandong conventionally powered?
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Carriers are ships intended to project power. The USA sits on a continent without any nearby enemies. So, American military doctrine is expeditionary in nature. The assumption is that if America fights a war, it will be abroad and therefore it needs the means to project force abroad. Therefore, a strong navy with a nuclear powered carrier element was seen as fitting this doctrine.
There is no doubt that China has the capability to field nuclear powered aircraft carriers. The question is whether it is in line with their military and political doctrines.
In the near term at least, the main foreign/military issues facing the Chinese Communist Party are Taiwan and projecting power close by, like the Spratly Islands. For these purposes, conventional aircraft carriers with airstrips on artificial islands, along with anti-ship ballistic missiles, hypersonic cruise missiles and stealth fighters are sufficient to deter foreign intervention.
Nuclear submarines are something else - they pertain to the strategic nuclear deterrent and this deterrent is most effective if their cruising range is effectively unlimited, and of course nuclear powered submarines are air-independent. The idea being that it is entirely possible for a nuclear submarine to stealthily park itself close to a hostile country and launch missiles, with which there will be very little warning before impact.
Incidentally, read up about the Chinese Belt & Road Initiative, and how China is building infrastructure to connect itself to Africa and Europe. The contrast is interesting to behold, how one country is building walls and alienating allies, while another is building roads and expanding its influence.
As Solar Mike said, we do not know exactly what is going on in the minds of the Chinese government but we can judge them by their actions. Historically China does not pick fights with other countries and send its army to go impose their will on foreign lands. Their goal for now, at least, seems to be geared towards economic expansion.
Lastly, if you look at the composition of the Chinese politburo - you will see that they are scientists/engineers/lawyers/economists/etc. Their country is led by people who think, and do not shoot from the hip. Any Chinese foreign policy decision that is made, you can be sure there was some thought and deliberation behind it.
I'm not an expert on this so this is an "educated guess".
It boils down to what the advantage of nuclear power is. To laypeople it sounds cool, but for the military you need a tangible advantage. That advantage is (see the Wikipedia article on nuclear submarines):
The performance advantages of nuclear submarines over "conventional" (typically diesel-electric) submarines are considerable. Nuclear propulsion, being completely independent of air, frees the submarine from the need to surface frequently, as is necessary for conventional submarines. The large amount of power generated by a nuclear reactor allows nuclear submarines to operate at high speed for long periods of time; and the long interval between refuelings grants a range virtually unlimited, making the only limits on voyage times being imposed by such factors as the need to restock food or other consumables.
Current generations of nuclear submarines never need to be refueled throughout their 25-year lifespans ...
Compare that to aircraft carriers. Aircraft carriers can't submerge, so being completely independent of air isn't an advantage. That leaves the other advantage, which is to operate at high speed for long periods of time. This particular advantage is really only useful when you are projecting power - in other words when you are operating far away from friendly bases.
So it comes down to whether the Chinese government wants to pay more money for the ability to project power. The fact that the Shandong is conventionally powered indicates the answer is, for now at least, "no" - they aren't interested in sending ships across the Pacific Ocean.