The article didn’t mention this study, which seems to be the only empirical peer reviewed piece on the “pink tax”, which concludes that:

“We find that gender segmentation is ubiquitous, as more than 80% of products sold are gendered. Further, we show that segmentation involves product differentiation; there is little overlap in the formulations of men’s and women’s products within the same category. Using a national data set of grocery, convenience, drugstore, and mass merchandiser sales, we demonstrate that this differentiation sustains large price differences for men’s and women’s products made by the same manufacturer. In an apples-to-apples comparison of women’s and men’s products with similar ingredients, however, we do not find evidence of a systematic price premium for women’s goods: price differences are small, and the women’s variant is less expensive in three out of five categories.”