It should not take until the mid 2030s for China to get a nuclear carrier.
Around the middle of this decade or slightly after that the technologies should be in place I think.
I wouldn't be surprised if work has long been going on on the nuclear drive train. Of the 20 to 15 years that are needed for this, 10 to 5 years should have passed by a long time ago.
This is work that takes place somewhere in China in closed factory halls, we don't see anything before that.
Only in the last 5 years of this process you need the hull in which you want to install everything.
There should be no doubt that for a strategic defense program such as carrier, the development of key technologies have long been underway for many years now. We know that's how China does strategic planning and development. China had in place a three-step career development plan; nuclear-powered carrier being the last step.
For nuclear-powered carrier, the appropriate nuclear reactor is really the only key/obstacle above beyond 003. We know China has very solid nuclear technologies and industry, which include both civilian and military applications: nuclear power, nuclear weapons and nuclear submarines. So the capability to provision PLAN with a working nuclear reactor including output level, safety and enrichment should not be a problem. I think China is setting the bar much higher than when the US started to development its nuclear powered carriers. For a close analog, think about when China develops its first CATOBAR conventional carrier 003, its benchmark was not Kitty Hawk, but Ford in many ways.
By the way, I read report in Chinese media over a decade ago by certain lead nuclear engineer that ACP100 was developed out of military reactor. May or may not be true, but does tell you that it's highly likely the reactor has been under development for quite some time now.