EDIT: Forgot the big rig part. The answer to that would likely be that the big rig would not be permitted to pull off the road onto the shoulder to permit anyone to pass. They'd likely have to wait for either a divided lane, or, a proper turnout of sufficient length and breadth. Many turnouts I see in the country are short and not typically designed to facilitate big rigs.
Some of these issues are subjective, and almost all of them are CHP issues. How *I* might see them or choose to enforce them could be irrelevant, because turnouts and country roads/highways/freeways tend to be CHP enforcement issues and not for the municipal cops or deputies. I cannot say what their marching orders might be on such matters, and I do not come into contact with many CHP officers these days.
I think the CA-46 one includes the gravel part beyond the road shoulder. There are certainly stuff on Route 20 with a similarly large, yet paved, area and signs that tell slower traffic to use the turn out.
They were just examples someone ELSE posted in this thread. What if the one was a bigger PAVED one? In fact the one on SR20 shows trucks parked in it in the aerial (but not the street view). They do however seem to be far enough from the white line that another vehicle could use the turnout to allow people to pass.
So, the only real answer to the question about whether or not someone can park in a particular place adjacent to the main roadway is, "It depends ..."
I may not always be right, but I am never wrong.