This rule also applies to photons reflecting from mirrors. The photon is reflecting from the mirror, and the electromagnetic field is varying regularly and smoothly changing from the incoming to the reflected wave. The transmitted wave doesn’t exist, so the amplitude is a happy zero.

Then the mirror is yanked away. The reflected wave’s amplitude abruptly drops to zero, and the transmitted wave suddenly jumps from zero. Those are two sharp transitions that require a lot more bandwidth than the original photon had. Our photon that has been cut off is still in a superposition of reflected and transmitted. But it also has a sharp edge, which requires a multitude of photons at different frequencies.

Cutting a photon in half generates a rainbow. And as far as I can tell, the generated photons are in a superposition of both reflected and transmitted light. But since there are potentially many photons, both transmitted and reflected light could be measured simultaneously.