What does {ggdist}'s stat_interval levels calculate (I thought it was confidence intervals but they're not correct)?

I'm using ggdist (which is awesome) to show variability within a sample. I have a series of means, SDs, and std.errors and I want to use the stat_interval() function to show the 50%, 80%, 90%, and 95% confidence intervals of these samples. It seems that they're calculating something different because the intervals being plotted are very different to when I calculate confidence intervals manually. Does anyone know what I'm doing wrong / what the function is doing?

The 95% CI of Sample 1 in the attached plot should be from 39.38 - 39.62 but it's being plotted much larger (nearly 38.5 - 40.5, see image).

Reprex ↓

library(tidyverse)
library(ggdist)

 data <- tibble::tribble(
            ~n,          ~mean,     ~SD,       ~se,
           "Sample 1",    39.5,     0.5,    0.0625,
           "Sample 2",    39.4,     0.6,    0.0750
           )

 data |>
   ggplot(aes(xdist = dist_normal(mean, SD),  y = fct_rev(factor(n)))) +
            stat_interval(.width = c(.5, .8, .9, .95), position = "dodge")

I believe the ranges being plotted are simply the quantiles, not confidence intervals. e.g.:

> quantile(rnorm(10000, 39.5, 0.5), c(0.025, 0.975 ))
    2.5%    97.5% 
38.49979 40.46578

For confidence intervals, I think you are looking for Students T. e.g.:

data %>%
  ggplot(aes(xdist = distributional::dist_student_t( 63, mean, se),  y = fct_rev(factor(n)))) +
  stat_interval(.width = c(.5, .8, .9, .95), position = "dodge")