Does China have any analogues of vertical take-off aircraft? Here I am watching the F-35 take off from the Japanese JS Kaga, effectively turning the helicopter carrier into a full-fledged aircraft carrier, and no catapults or kilometer-long springboards are needed. The conventional Type 075 could be like this if there were similar aircraft:
The word "effectively" is doing a lot of heavy lifting here. While STOVL fighters look good on paper, they have to make a lot of sacrifices to performance to function at all. Just look at the F-35B. It's a single engine fighter with low payload and low range. It's not at all the kind of plane that the Navy would want, and you'd only want to use it if there's no alternatives.
A ship like JS Kaga can only carry about 6 of these planes so it's a very far distance from being a full-fledged carrier. And generally speaking, the only reason to have light carriers is that some countries can't build and operate full sized carriers. China is not one of these countries, so this does not apply to them. The other reason is that you are running so many military operations that you need more carriers than you have access to full-sized ones. The only country this applies to is the US - China has no interest in expeditionary wars so it doesn't need undersized pseudo carriers. And if the PLAN really wants some pseudo-carriers, they can just stick some J-35s on 076 and call it a day.
For your actual question, China is exploring the concept of STOVL fighters, but there's no indication that they have built any demonstrators yet. I suspect that they will find this technology limiting enough that they won't do much with it.