One of the problems with a STOBAR carrier is that the head wind needed for the lift is in part being obscured by the ski ramp. The difference in take off weight between catapult launch and ski ramp can be significant. We have never seen a J-15 taking off fully loaded from the Liaoning. Only with 4 AAM or with two bombs. I think with a ski ramp launch you have to make compromises between weapons load and fuel. Something you don't have to do with a catapult.
I think on a STOBAR carrier an aircraft is limited in payload if it is being launched at certain lower levels of headwind, but that at higher headwind it can definitely launch heavily loaded fighters.
I've read around this topic more and more over the years, and I think the ski jump vs catapult issue has been dramatically oversimplified, and that the issue is not about whether a ski jump can or cannot launch an jet fighter which is "heavily loaded" compared to a catapult but more about how reliably a ski jump can launch heavily loaded fighters in, and how many conditions and situations that can be done in, vs a catapult.
(to copy one of my posts in a different thread)
I believe what catapults offer is the ability to more reliably launch heavily loaded fighters under a variety of conditions (including minimal head wind) as well as if a fighter's engine fails during a launch, thus making a catapult safer and more flexible in launching fighters compared to ski jumps.
Catapults also of course are the only reliable way to launch aircraft like fixed wing AEWC, which a ski jump likely cannot do.
Catapults therefore offer a far greater margin for safety and flexibility when launching heavily loaded planes than ski jumps, but that does not mean ski jumps cannot inherently launch heavily loaded planes.
As for us not having pictures of J-15 fully loaded -- that's a valid but weak argument, I think, considering this is the PLA we're talking about. Lack of physical evidence is not evidence of lack of is basically one of the key mantras here.
More important for the J-15/Su-33 is that Russian aviation authors have come out and directly said that Su-33s were able to launch at MTOW or near MTOW from Kuznetsov during tests, and if you go onto any Russian language military board they will say the same.
And of course, there is also this:
https://www.sinodefenceforum.com/stobar-aircraft-ski-jump-performance-su-33-j-15.t8043/
I think the entire "ski jumps cannot launch heavily loaded planes" cliche has become a bit of an oversimplification by most journalists in defence media, rooted partially in bias and partially because it sounds "right" (even though it's not), similar to how J-20 is often always mentioned to be "thought to be developed with hacked F-35 data" or "stealth developed from crashed F-117".
The label "training carrier" is of course misleading because its a label being put on the Liaoning for political reasons. It has to do with the way they got hold of the Varyag hull. But the most often heard phrase for the Liaoning is "starter carrier". The new Type 001A carrier will not have to deal with those kind of issue's. So its possible that the pennant number will not be 17.
So you're saying you think 001A will not get CV-17 as a pennant number because CV-16 has been deliberately chosen as a "training carrier" or a "starter carrier" pennant number?
I must say that's a variation of the position I've never heard before, but I also think it's not very likely at all.
It is far more likely that CV-16 is just the actual pennant number of Liaoning ascribed as part of the first carrier for the Navy, and they're just happening to call it a "training carrier" or a ship for conducting "scientific experiments," as they are learning to operate carriers and develop the expertise in the first place.
But it's not like they're going to be obliged to change the pennant number of CV-16 if they want to operate it as a standard warship eventaully.
So no, I don't think there are any strong indications at all to argue that 001A would not be CV-17, or that CV-16 is some sort of designation given to Liaoning because of its supposed temporary training carrier or starter carrier status.
The key thing we should be looking at is the ship itself, and there is nothing about it which suggests to me that it has been fitted out for anything less than having the capacity to act as a fully functional warship