Why is the variance of the Wright-Fisher model not equal p(1-p)/(2N)?
The binomial variance $2N p (1-p)$ is for the number of individuals $n'$ carrying the allele in the next generation. The frequency of the allele in the next generation is $p'=n'/(2N)$, so its variance is $$\text{Var}[p'] = \text{Var}[n'/(2N)] = \text{Var}[n']/(2N)^2 = p(1-p)/(2N).$$