Perhaps the cowboy-style clothing derives from the specific customs of the Garundi Ustradi clans who founded Alkenstar. According to the Impossible Lands book, the clans’ customs and values influence modern Alkenstari society, and the book shows a picture of Ancil Alkenstar---who it notes was taken in by the clans---in cowboy-style clothes. Impossible Lands also emphasizes that everyday wear in Alkenstar is pragmatic, so it’s conceivable that this is the style of clothing that was the most pragmatic for this particular geographic location.
As for the more Victorian fashion of the elite: Impossible Lands indicates that Alkenstar’s ethnic composition has changed over the years due to the duchy’s “aggressive courtship of migrant laborers and the affluent from across Golarion,” with the Ustradi clans absorbing customs they found useful into their society even as the Ustradi remained the duchy’s wealthy elite. Given that Impossible Lands seems to indicate that the duchy tries to retain some degree of independence from both Nex and Geb even though it is technically a duchy of Nex, it’s possible that the Ustradi, as they grew wealthy over time, looked to absorb the customs of elite outside of Garund for their fashion, particularly to the extent that the peoples of Avistan migrated to Alkenstar.
Notably, the Agents of Edgewatch AP has art depicting what appears to be a Victorian style of dress for Absalom. So it’s conceivable that, to the extent the wealthy Ustradi of Alkenstar---who seem to consider themselves to be excellent merchants---looked to absorb the culture of areas of the Inner Sea regions beyond Garund, they elected to adopt the fashion of Absalom, one of the greatest trade cities in Avistan.
Then again, perhaps none of this adds up. (For example, art in other books doesn’t seem to suggest that Absalom fashion is Victorian in style.) Personally, I agree with what Mathmuse recently said in the “Why Most Inner Sea Nations Fail” thread. As he opined: “The true out-of-game-reason is that the writers and artists want us to recognize Alkenstar was a Wild West setting with steampunk elements, so the residents dress like Wild West setting with steampunk elements.”
