are modern AAMs even designed to hit aircraft that high and fast and can still turn like a fighter?
For what it's worth, in air that thin, absolutely nothing turns like a fighter lol. Modern AAMs can indeed get up there and prosecute though. As a general rule of thumb, in practically all relevant flight regimes, modern AAMs are more kinematically capable than their target.
It's naturally already hard for any fighter jet to obtain weapon grade tracking on J-36. But it's even harder to do it in look up mode.
I'd note that the signature characteristics of J-36 remain very close to the PLA's chest, and that while I obviously understand where you're coming from, I would be hesitant to make the former claim quite so definitively. I mean nothing other than what I say by saying this, but advances in sensing have quite substantially outpaced advances in signature management over the past couple decades.
On the second point, look-up is actually the easier of the two when compared to look-down engagements, so the high elevation doesn't constitute a significant factor in ease of acquisition.
it is even harder for something like AAM to lock on to J-36 looking up and facing strong EW pressure and flying at > mach 2.5.
Regarding the speed, there are imo a couple of noteworthy considerations to address first.
For starters, while I have zero doubt that 36 has ample giddyup in its step, >M2.5 is a veeeery high bar. There may be envelopes wherein it achieves those speeds, but I strongly suspect that figure will be substantially beyond anything the aircraft sees during 99.999% of operational sorties (both peacetime and potential wartime).
For starters, maneuverability in high-supersonic regimes is best described as "lumbering," and one trait no pilot has ever desired during the inbound leg of his CAP orbit is a pull-off turn radius measured in
eventually's. Thus, even at its face, the most desirable envelope during operational tasks is likely found in the high transonic to low supersonic (1.2-1.5, just after the worst of drag-divergence subsides) regime depending on a myriad of factors.
Secondly, an object's thermal signature at M2.5 - even at 20km altitude - is going to be quite substantial, which bodes poorly for a platform with a major/primary design focus on signature management. Coupled with this, the impact on airframe readiness and longevity from extended periods at this speed is easy to identify; thus, even should they be achievable at any given time, it's highly unlikely that the capability sees frequent or prolonged use - especially during an air to air engagement. A more likely use case, assuming there is one, would be in a scenario involving either a need to
very expediently go from being "here" to "not here" (i.e. evading a launch from another platform) - a scenario I find largely dissonant with the role and environment I expect to see 36 find itself in; or in a uniquely rare instance where a specific sequence of events places the aircraft in position to accomplish some mission/task/goal if and only if it employs its absolute design top speed, despite the margins for such things seldom falling within such thresholds. At the end of the day, a few hundred m/s on top of ones' current airspeed is rarely meaningful when examined at larger scopes - stuff like chasing down an enemy aircraft or stretching an out of position aircraft's legs for a stray shot is pretty much always either a bad idea regardless of whether you eventually get there, or was already possible given the capabilities of the pursuing aircraft. There's a reason most jets have converged on pretty similar kinematic performance.
As far as EW pressure goes, this is imo a poor representation of how EA impacts signature dynamics. Funny enough, by virtue of the unique envelopes wherein 36 seems likely to operate, there will be relatively fewer opportunities for offboard electronic effects compared to aircraft flying more conventional profiles; and while there certainly are a lot of neat things jammers can do nowadays, modern phasers are really really reluctant to bite on onboard angle deception jamming, and most range deception techniques are quite a bit less effective than they were some 20+ years ago due to a variety of factors which lend themselves poorly to discussion in this setting. Of additional note, certain supplementary countermeasures - most obviously, towed decoys - would be put in rather a bind should the aircraft employ them while hanging out at M2.5+ (it will rapidly evolve into an un-towed decoy, and eventually into a land-based one).
Overall, I would just encourage commenters to take note of the fact that altitude is not at all the hard part in these engagements. Launch platforms are in quite thin air to begin with (taking the hardest part out of the equation), and while a higher altitude target is challenging in its own ways, the even more rarified atmosphere at those altitudes will - if anything - probably amount to similar or superior cross-range performance in plenty of profiles. The way to shave range off a missile is to get down into the thick and soupy air, not to hang out as a functionally straight-line speedster in the land of minimal drag.