A few things going on here, but let’s see if we can sort through it. From my understanding you’re after the heights of the polygon only (the boundry points, or even calculated points along it), or you’re after the heights of points inside (and possibly including) the polygon.
The answer to either of these are, yes, they are available, basically through two methods; sampleHeight() and sampleHeightMostDetailed(). You send them an array of your coordinates, and it will return an altered version of the array with the height adjusted.
So, the trick is how you create those coordinates. The simplest is to use the polygon itself, maybe calculate extra points along it. But what I think you’re after is to create a grid on the inside, and use those? Maybe for volume calculations, etc.
Let me know what you’re trying to do with the coordinates, maybe I can help from there. As I said, the mesh in the polygon isn’t (as far as I know; don’t take it as gospel, as there are many nooks of Cesium I don’t know much about) available, but you can recreate it. I do something similar where I create a grid inside the polygon and sample all those points. Keep in mind, this is a costly operation and takes some time, depending on your machine and hardware. SampleHeights() is the quickest as it gives you current values from the what you’re seeing, while SampleHeightMostDetailed() makes sure the data gives you the most accurate (slightly slower, depending on your zoom levels and what’s in the raster cache).
In your screenshot, is the mesh the red color blobs? One thing to note about sampling on a pointcloud is that there is a percent chance your sampling falls through the pointcloud to the ground, so you might see lots of reasonable heights and some that are at the height of the ellipsoid (or terrain, depending), so you might even filter (or resample) those as you go.