Top tongue-in-cheek directors: Wes Anderson and Wen Jiang. Asteroid City isn't my favorite Wes film, but it's surely tongue-in-cheek and pretty damn funny.
This movie reminds me a little of Tennessee Williams, the all-time master of damaged and traumatized human psyches. I see this work as a treatise on human issues, especially the labels given to us by others and those we give ourselves, and how they affect one's life and relationships.
The partial view of the "Confessions of a Narcissist" marquis that showed up in the background of the tet-a-tet between Augie and his almost-onstage-wife is a clue. The term "narcissist" didn't become popular psychology until the 1980s. There were other anachronisms, but this one is particularly striking in context.
And what's with that song and dance number in the middle of the show? The band that showed up in this desert had no other raison d'etre!! Did Wes just reference the Time Warp from The Rocky Horror Picture Show??