Both things are true: there is a period of maximum dynamic pressure, and there is a pressure rise between ~M0.8 and ~M1.2. Sometimes they are the same occurrence, sometimes not. Successful recovery requires withstanding both
There are parts of the airflow in this transonic regime that are supersonic, and there are parts of the airflow that are subsonic, and there are shockwaves forming and collapsing here and there, mostly around things that stick out and/or have square corners.
All of this causes stresses on the airframe that are different to those experienced when it's all subsonic or all supersonic. A lot of this buffeting compresses against the tip of the nosecone which isn't usually much of an issue; but when it causes fins to start fluttering they often decide to tear off in a big hurry.
A LaserLoc163, for example, will break mach on almost any 38mm J, many I's, and a few H's as long as you keep the weight down. I might shy away from the CTI i540 or Loki K's though
At the other end of the spectrum, of course, you can buy a carbon kit and an L2200G