That's why the STOBAR J-15s rely on buddy refueling after take off. They may still require buddy refueling even with CATOBAR carriers if even superhornets often require that depending on payload.
I doubt the optimal perfect A2A payload and performance trade off is at 2x fox 3 and 2x fox 2. I'd say for heavier fighters like Flanker series, it should easily be stretched to at least 4x fox 3s. Two high thrust class turbofan engines and all that lift and fuel. The flanker series are capable of carrying 10x fox 3s and 2x fox 2s... obviously with significant range and performance penalties. The biggest advantage is it doesn't require fuel tanks to still retain best in class range. What a fantastic bird. It doesn't matter how it's measured but the flanker has far better overall range and energy along with payload capacity than superhornet and F-35. CATOBAR will improve its energy and potentially reduce the need for buddy refueling.
J-15 has been shown on video to take off from 001 with four medium range missiles and two short ranges iirc. There were also photos of take offs with two YJ-83 and two dummy short range missiles.
The problem with such heavy fighters carrying only 2 fox 3s is that both are very likely to miss and not do much more than A2AD for a short margin of time. The difference between equipping them with 4 over 2 could be the difference between scoring absolutely no kills and scoring 1 kill for every four fox 3s, you gotta defend approaching missiles which demand fuel and performance from your aircraft and not firing anything at adversary aircraft really is just giving them too much advantage. It actually is very important how many missiles your fighter can carry with reasonable performance. I'd say with flankers, part of the great appeal is that it retains so much range and performance while carrying more missiles than lighter fighters and even peer heavy weight fighters. It can probably take off from CATOBARs and then refuel with 8x Fox 3s and 2x Fox 2s.
This is partly why China clearly intends to upgrade J-15 for CATOBAR carriers of the future and I suspect has desire to "replace" them with J-35. They will fly alongside because J-35 simply have a different set of skills and nowhere near as much payload and energy as the J-15. They want a modern day equivalent of the F-14 with overlapping roles but far better agility and maneuverability than the Tomcat.
