quantum chemistry - How can special relativity account for the electron orbital clouds of (stationary) heavy elements when electrons don't orbit in a classical way?

Einstein's famous mass-energy equivalence equation is still used for calculations, but still often considered less physically meaningful since the atoms that comprise a material don't actually gain more...atoms as the object increases its velocity. Or do they?

Despite the revolution in quantum physics that shows the motion of electrons around atoms isn't, in any way, actually like a planet orbiting a star, for some reason this doesn't seem to stop actual graduate scientists from continuing to conform to this inaccurate planet concept.

Multiple chemistry professors I have encountered, as well as apparently people like this fellow continue to state that this mass-energy equivalence is responsible for effects in heavy atoms under classical descriptions of velocity, and it turns out that these assumptions are somehow accurate.

So, if it is already established that electrons don't actually orbit a nucleus in a classical manner, how exactly is it that their "speed" around a stationary nucleus (with respect to the lab frame) can exhibit these localized special relativistic effects? What exactly is velocity supposed to mean in this context?