In my opinion, I don't see the need for China to have a nuclear powered aircraft carrier, unless one of two things happens:
1. China adopts a US-like global military strategy.
2. China develops a new nuclear propulsion technology that make it extremely cheap, such that it would significantly reduces the overall coat (procurement cost plus usage cost plus disposal cost) by going nuclear.
So far, I see China only adopting an East-Asia-only (or indo-west-pacific only) military strategy, in which it has no intention to extend its capabilities beyond the East-Asia (or Indian ocean plus west Pacific ocean). I see this as extremely potent and clever grand strategy.
I think even if China adopts an "East asia only" or "indo-west-pacific" military strategy, there are still significant marked benefits that a nuclear powered super carrier offers beyond a conventional carrier.
These benefits, IMO are primarily in relation to endurance.
Endurance matters in terms of not only the ship's ability to stay at sea, but also the ship's ability to carry more aviation fuel as a part of its overall tonnage, both of which can significantly reduce the ship's frequency for replenishment.
There is also the kinetic factor where a nuclear powered super carrier will be able to maintain top speed for much longer than a conventionally powered super carrier, which even in a high intensity regional war can be very important for entering and exfiltrating a theater of operations in the western pacific.
And even during peacetime, the ability to allow a carrier to be at sea in the western pacific with significantly reduced refuelling requirements offers greater redundancy and flexibility than a conventionally powered carrier.
... Whether the PLAN will eventually procure nuclear powered carriers or not is obviously going to depend on the balance of those factors versus the opportunity costs of procuring other systems that are relevant for their overall national and naval strategy.
But personally I think the PLAN are still intent on nuclear powered carriers as an eventual end goal.
Nuclear powered super carriers are not just weapons or war, but also ships of prestige that signifies a certain status of superpowerhood.
China sending out naval ships
China sending out conventional carriers
China sending out CATOBAR nuclear powered 80,000 tonne carriers
are three different levels of statement.
That is true, however nuclear supercarriers are sufficiently costly and complex and demands national resources to an extent that no nation would procure them without having self assessed military requirement for them.
If the PLA decides that they want nuclear powered carriers, it will be because they have a firm and clear military requirement for them first and foremost. Any benefits in terms of geopolitical signalling would be secondary or tertiary.