For Proportion Distribution, why SE = sqrt(p*(q)/n)?

lecture video 9, lesson 1, week 4, Confidence intervals for proportion
in proportion distribution, we have,
mu or mean = p
std = sqrt(pq/n).
but as i know from central limit theorem,
SE = std/ sqrt(n).
then why I found that SE = sqrt(p
q/n). which is the same as std.
anyone can explain this? for me, following central limit theorem formula,
SE should be equal to sqrt(pq/n^2) = sqrt(pq)/n.
anyone can explain what I miss?

Sorry for the late reply.
Were you able to find an answer to this issue?