From family in the navy, I hear they're currently short on radar technicians, both operating and servicing. Supposedly, ground based radar is facing the same issues. That fancy AESA radar does nothing if nobody is reading it or maintaining it.In terms of instructors and training they actually have more than enough for the roles. Especially pilot training, where Chinese pilots now get more hours than pre-covid US, which obviously had more hours than current US.
It's hard to tell exactly how integrated the branches are, but at least one indicator is that they can do inter-service CEC under combat conditions. That might not sound like much, but most NATO militaries cannot do it, more or less only US.
It's platforms and manufacturing lines which makes the main bottleneck. And in terms of navy and airforce, more raw numbers in recruitment is needed as well.
What they have currently is very good quality wise. What is needed is more of the same, but in much larger numbers. More J-20s, more destroyers, more drones, more missiles, employed with similar tactics and trainings as established doctrine.
Perhaps there needs to be better motivation to enlist for highly skilled or specialized roles.