Why does logistic/poisson regression in R give z-values while linear regression gives t-values in the summary output? In general, z-test is used when the population variance is known, but I am finding it difficult to translate this to the (generalized) linear model context.

I saw somewhere (as well from the comment below) that the reason is: the dispersion parameter for the linear model is $\sigma^2$ while the dispersion parameter is 1 for the logistic/poisson regression. If this is so, I would like to understand more mathematically why the value of this dispersion parameter leads to using z-values or t-values.