Since this article was posted on a blog advertising skin care products, I decided to further research this claim through other institutions that don't have a profit incentive. However, this article was written by a Physician Assistant with qualified degrees and knowledge on skincare and cosmetics, so it is fair to assume she has credible information.
The first source I looked through to verify this claim is UCLA Health, and the study they conducted with the UCLA School of Medicine. This study is also linked in the original article. Through this study, the chief of the clinical nutrition division concluded that avocados are beneficial for your skin, but more-so when they are consumed rather than used as surface level products. They conducted a controlled experiment over 8 weeks to compare skin elasticity in women. It is worth mentioning this experiment was only conducted on female subjects, not a random selection, and they said the results may differ for male patients based on hormonal differences. Since the avocado diet improved the overall health and fiber of the patients, this in turn affected their skin types positively. However, these results may not have been the same from avocado products like face masks and oils, which are advertised in the original article.
The article from UCLA Health about the results: https://www.uclahealth.org/news/article/eating-an-avocado-daily-increases-elasticity-and-firmness-in-skin-study-shows#:~:text=After%20eight%20weeks%2C%20the%20subjects,facial%20skin%20of%20healthy%20women.
The National Library of Medicine on the same study: https://pmc.ncbi.nlm.nih.gov/articles/PMC9786235/