If this thing has a 8-9 meter long weapons bay, a scramjet cruise missile launched at apex altitude and maximum speed (maybe Mach 2.5 or even higher) with very good range could be a serious possibility.
Okay,
I'm not sure about this.
Just think about utilization.
So I'm looking at this from the perspective that it can fly at really high altitude and cruise at high speed. Making it harder to hit by opposing AAMs and pick up by opposing radars (since look up range is normally less IIRC).
Flying high and launching fast means something like PL-17 can travel long distance at high altitude and using relatively little energy. There by extending its NEZ.
So you can have loyal wing man operate further ahead and working together to detect enemy fighter jet. Once locking down the opposing target, you can launch both PL-17 from J-36 and something like PL-12/15 from UCAV at target. Not saying that this is necessarily optimal, but my point is that J-36 property makes lobbing PL-17s from far out an optimal approach to keep it out of harms way.
By staying out of way, it can essentially lock on to target longer so AAM doesn't have to necessarily have to lock on to a LO target (which might be quite difficult).
Also in terms of attacking with hypersonic, I think it's better installed on other platforms. For example, anything with 2IC can be attacked by DF-26. J-36 being closer to target may be better off providing targeting guidance and providing hiding EW against targeting carrier.
Aside from that, it could be part of a wider attack where J-36 coordinates its UCAVs to launch different types of attack munition from ARM (or maybe it launches that) to AShm to maybe even PGMs.
Or maybe even something like MD-22 coming and J-36 coordinates it to perform hypersonic type of attacks.
I don't think it makes sense to put something as large as hypersonic missile inside J-36 when it can safely get closer to aircraft carrier with attritable assets in front.