One answer to this question explains that "velocity of electrons has no meaning" while another says that "it can be argued that they don't move around atoms at all". And then in another post it is answered that electrons in atoms do indeed have a speed associated with their kinetic energy. Granted, speed is not velocity, but is the expectation value $\langle\hat{p}^2/m^2\rangle$ not what one can think of as akin to a classical "speed" (squared). Is a measured value of $\hat{p}/m$ not akin to a classical velocity* (or can this not be measured, not even a probability distribution)?
How is (a chemist) to think of angular momentum of an electron in an atom (specifically orbital angular momentum)? How completely should one abandon the classical idea of velocity as part of momentum when discussing quantum particles? This post has an answer that provides a geometric argument about "transforms under rotations". Isn't there a more (classically) appealing picture?
$*$ ignoring relativity
Best Answer
Velocity is an observable in quantum mechanics. For a massive particle, the velocity operator is the momentum operator divided by the mass. Eigenstates of energy in an atom are not eigenstates of velocity. If you prepare a hydrogen atom in a state of definite energy, then measure the velocity of the electron, you get a random vector that has a certain probability distribution. The mean is zero.
I don't think any of this really contradicts the statements you list from the other places on this site. Those statements may appear to contradict each other, but that's because they're using imprecise language. When you use English to talk about quantum mechanics, it doesn't necessarily fit.