Thank you for your extensive response! And thank you for the example question; this is definitely already a proof of concept for my colleagues.
For the popup: as we are using Safe Exam Browser, I was hoping SEB would understand the draggable popup as a new tab, which can be easily accessed via the bottom left SEB icon, but unfortunately it didn't understand it this way. However, I have also talked to CTO of GeoGebra mentioning there's no general solution to use a BYOD-laptop with GeoGebra as calculator during a paper exam. In my talk with the CTO (
Michael Borcherds) he mentioned there might be an
exam.geogebra.org coming where appending different parameters could modify what functions are available, like enable3d, graphing, ... This could easily be added to SEB without Numbas, but also with Numbas as a simple link which opens in a new tab. I will forward this discussion to GeoGebra, in case they find it interesting.