It was 'leaked' years ago that they were going to make two CATOBAR carriers of the conventional propulsion type and after those they would make nuclear powered carriers. So Type 004 should be similar to Type 003 and is likely under construction as is.
I don't know why you assume they'll wait until they test 003 to make the next carrier.
Also, the 2030 deadline if anything seems overly pessimistic considering they have already built the new construction facilities at Shanghai which is half the work and have the Type 003 already half built. I assume there will be a small delay while they evaluate 003/004 but I wouldn't be surprised if they were designing the successor ship already.
I think the political purge at the Dalian shipyards is the likely culprit for the delays in the construction of Type 004.
I suspect the original plan was to have a more conventional design built at Dalian with steam boilers and steam catapults as a backup. But given the high state of readiness of the EMALS catapult and China's advances with gas turbine propulsion it is quite likely they changed the plans. So that probably put the kibosh on things there.
I doubt it, we never had any solid guarantee or predictions for how quickly the carrier following 003 (i.e.: the second expected conventional CATOBAR) would emerge, nor any solid predictions for whether it would be built at JNCX or DL.
And if you're talking about Sun Bo, his example of graft was probably legitimate and the word "purge" is frankly a dramatization, and much of the English language media's association of him as being "in charge" of carrier 002 is a bit laughable tbh. At his level he was in charge of far more shipbuilding projects than the carrier alone -- and likely far more commercially lucrative projects than the carrier -- and it would have been graft in general that took him down.
My personal belief is that after CV-16 Liaoning was refit, the PLAN wanted to move onto a CATOBAR carrier, but the PRC leadership was more cautious, so they ordered 002/CV-17 Shandong first, which Dalian built.
At about the same time leading up to the order of 002, I suspect the PRC and PLAN leadership were assessing advancements in technology namely the EM catapult while actively working on the design and the industrial side of how building a large CATOBAR would work.
If there was any "delay" in the construction of their first CATOBAR carrier, IMO it was the decision for steam versus EM catapults, as the PLAN likely recognized EM catapults were their future, and that if they pursued steam it would be a technology that was already on the way out and would either have to be refit on any carriers it was installed on -- or a system they would have to continue to support for a ship's given service life.
That's why they proceeded with the EM cat vs steam cat competition in the mid 2010s, while likely actively doing the redesign work for the CATOBAR carrier (that we would come to know as 003) if the EM cat won. In any case, the EM cat did win, and thus they proceeded full throttle with fabrication and construction of 003 at Shanghai.
Regarding 003's propulsion, I do not think it will be powered by gas turbines, but rather using steam turbines.
My understanding is that 002 and 003 will share the same steam turbines and similar other elements of their propulsion (003 might have more boilers or more powerful boilers).
As far as powering the EM cats go, they probably have separate generators for that which will also provide electricity for the rest of the ship's services and major subsystems too.
But the prime drivers will be steam.
That is to say, I do not expect 003 to have IEPS.