This has already been done, and there’s already some sort of extension available
Yes, the Pedicle Screw Simulator extension does exactly this:
I don’t think you need to use this extension for your project, because your models are different, you position them differently (in current Slicer versions it is very easy to position models using interactive transformation handles) and it takes just a few clicks to copy CT values to the model points.
If not, whether it’s feasible and a reasonably achievable goal for someone with some (but not extensive) experience coding in Slicer
You don’t need any coding to get started. If you want to streamline the processing (minimize number of clicks) or fully automate it then you can do that with Python scripting. If you have specific questions you can ask questions here, or for getting more substantial help or developing complete solutions you can contact Slicer Commercial Partners.
If there are any existing extensions or functions that would give me access to vertex points on a registered surface model, and allow me to then probe the nearest voxel for its intensity (HU) values
Probe volume with model module does exactly this.