planck length doesn't come up even once, it all boils down to these things: 1. electron has momentum, and from that follows it has a wavelength, and at the same time 2. orbit is stable, which means that after every "rotation" electron has to end up with the same phase, which means there is only a finite number of solutions to time-independent schroedinger equation for (hydrogen) atom (don't bother solving it on paper for anything with more than one electron) and these things are spherical harmonics

Planck length is not like universal pixels. It's just where current models say there's little reason to look at smaller things, since it's kind of like worrying about which flecks of paint are coming off a car in a racing video game. It's just ... so irrelevant as to be ignorable.

It's nigh impossible to have any energy that could interact with us or atoms on the Planck length scale that wouldn't just collapse in to a black hole. It's not so much any observation of real-world pixelation, and more that even to atoms, it's very tiny.