"Pretty Cure" has gone through numerous iterations, but at its core, it follows a group of teenage girls given magical items that allow them to transform into powerful warriors. They work alongside fairies to defend against evil monsters attempting to make Earth miserable. Similar to other anime of its ilk, it features extensive transformation sequences, as evidenced by the one for Cure Mermaid, as referenced by Diana Huh in the original tweet. As further evidence, YouTuber BrinaFlautist made a video of the "My Adventures with Superman" transformation featuring the music from "Pretty Cure."
While "Pretty Cure" was a direct influence, that scene draws heavily from magical girl anime as a whole. And that's not the only thing "My Adventures with Superman" has taken from this particular genre. In the first two episodes alone, there are parallels between Clark Kent and Usagi Tsukino from "Sailor Moon." For starters, they both accept that they have powers initially somewhat reluctantly. They just want to be normal and hang out with their friends, but threats from nefarious individuals force them into fighting. Clark Kent goes to great lengths to protect Lois (Alice Lee) and Jimmy (Ishmel Sahid) in the same way Usagi had to fight a monster who targeted her friend, Naru, in the first episode of "Sailor Moon."
These storylines and art style make for a unique Superman adaptation that hopefully flies high for a long time to come.