After much weeping and gnashing of teeth, I have found the solution.

The scatter3d function uses the spheres3d function from the rgl library, and this function was not working because on certain computers (like, in my example, the Lenovo Yoga Laptop), the default drivers do not support the version of OpenGL that the rgl library uses (this version being OpenGL 1.2), causing some functions like spheres3d to not render at all.

To fix this, you must directly install the newest drivers onto your computer. In my case, the Lenovo Yoga Laptop uses AMD graphics, so I had to go to AMD's website and install driver updates for AMD Radeon Series Graphics and Ryzen Chipsets, thereby fixing the problem. Hope this helps anyone who might encounter this problem in the future.