The chart is rendered as a .NET Client Control.
Yes, in short I'm looking to get annotations drawn by the user on the client side back to the server side. I'm open to your suggestion on implementation details, or letting me know if this is even possible.
The user draws an annotation using the exposed ChartFX annotations toolbar. I was hoping there was some sort of server-side event that would fire whenever an annotation was created or updated. Since I didn't find that sort of event in the documentation (does one exist?), I just used the chart click event as a convenient entry point for a callback -- in reality, I'd probably use SFX_SendUserCallback from javascript. The click event fired correctly (so my trust settings are okay), and all of the client-side chart state was correct on the server side, except for the chart.Extensions part where the annotations live. Since the client-side annotations weren't there, I postulated that I needed to enable ViewState for the Annotations; however setting ViewState to true didn't stick. I don't know if that is integral to the solution or not, and don't really care as long as I can get the client side annotations back to the server side.