Beyond the 1IC, I don't see a requirement for lots of AAM launches at a distance of 200+ km, because there just won't be that many opposing aircraft.
So there should be enough J-36 and UADFs to obtain control of the air, with stealth bombers focusing on destroying the airbases and carriers in the 2IC.
I see China acting to expand land based air superiority beyond 1st island chain. While we have PLARF reaching beyond 2nd island chain with anti-access, area denial, PLAN progress and programs indicate a desire to meet and fight USN far beyond 1st island chain. This effort comes with the support of PLARF but the missing component is all the other land based PLA assets. None of the land based cruise missiles that isn't HCM has range that can support this fight. So PLAN fighting USN beyond the 2nd island chain is on its own with only PLARF.
PLARF will need ship based assets to coordinate A2AD. Whether that's from ships feeding the data or ship launched aircraft, PLAN needs to be able to slug it out against USN so far from China's coast. Space based assets for sensor and guidance can't be guaranteed and resilience of these networks require PLAN to be actively present in this part of the world.
PLAAF doesn't have the range to go that far. UADF Type A and B can't fly from coastal airfields all the way out to 2nd island chain, fight and get back. That's nearly twice their operational radius. J-20 and land based J-35 can't either.
PLAAF and PLAN have supplemented shortcoming in PLAN size vs USN with ALBMs, H-6 and various hypersonic weapons but until PLAN can match USN numbers and carrier borne aircraft numbers, PLAAF needs to do some lifting too. A few squadrons of GJ-x performing air to air actually is a deadly addition in the PLA inventory. These will have the range to fly out to 2nd island chain, perform their air to air missions (possibly also anti-ship) and RTB.
If China isn't able to keep USN at around the 2nd island chain, US strike packages from ship and submarine launched cruise missiles, LRHW and air launched long range weapons could potentially begin threatening China's coastal military installations. Right now, the US doesn't quite have that range yet until near the 1st island chain but China should be pushing as the rising power. PLA has pushed US from
within 1st island chain to dominance only beyond to 1st island chain in the 2000s and since all the A2AD weapons of the 2010s and PLAN progress, now pushed US to the 2nd island chain. Since that A2AD network requires presence of PLAAF, PLAN or space based assets, it's best to continue pushing the US back.
It makes sense to bolster air superiority, particularly since right now it's only a handful of J-35s, UADFs and a few squadrons worth of J-15s on three carriers and a couple of UAV LHD carriers vs hundreds of F-18s + F-35s on half a dozen active supercarriers on USN side.