Be aware of different notation in stat_smooth/geom_smooth : fct = L.4
and in drm: fct = LL.4

It tooks me an hour to notice ...

So this gonna work as intended:

enter image description here

ggplot(test_data, aes(x = Conc, y = Response )) +
  geom_point() +
  stat_smooth(
    method = "drm",
    method.args = list(
      fct = L.4()      #←----------------------------------------------------
    ),
    se = FALSE
  )+
  scale_x_continuous(trans="log10")