Immanuel Kant uses hernach quite a lot in his writings.
However, here the word is said to be used only regionally; but I doubt that Kant would have used such words in his works.
Is it perhaps an archaism as considered from our perspective?
Yes, today, hernach actually is an anachronism. Everyone would nowadays say "danach".
If you consider the time Kant wrote his work, the word hernach would have been much more common than it is today. A quick look in Grimms Wörterbuch (1835) shows that da[r]nach is explained with hernach, but not vice versa (so hernach can be considered more common than danach), and a Google ngrams search shows that hernach was more common than danach until about 1840.
Today, the word is only used in a number of dialects.
... but I doubt that Kant would have used such words in his works.
In German language a lot of dialects exist which differ a lot. I've heard that some dialects even satisfy the criteria of being "languages".
According to the Wikipedia article about "Standarddeutsch" in the time when Kant, Goethe or Schiller lived a unified German language spoken all over Germany did not exist, yet.
As a consequence their works could not be written in "German language" but they had to write in one of multiple German dialects.
Ps.: Even today people typically do not speak the unified German language but the local variant of German (having own words and even an own grammar).