Yes, I ignored your references, because they were meaningless concerning whether there is continuous time/space at the smallest scale of the behavior of Quantum particles.
Of course there is movement of Quantum particles, but NO continuous time/space nor gravity.
Reference to the Hydrogen atom IS NOT at the Quantum level of particles.
OK, how about Peskin&Schroder's book on quantum field theory that is specifically about particle physics?
At no point in the entire book do they even consider anything other than a continuous spacetime. And that is an absolutely standard textbook in the subject.
So, yes, the standard references do have continuous spacetime. Thos that discuss gravity do so on a continous spacetine background OR are pure speculation.