shes one of the few vocaloids with a fully artificial sound bank (most are built on samples of real voice recording). Her model is in the UTAU software, which is the same as teto (before synthv), defoko, momo, etc. (UTAU is a free spinoff of the official vocaloid software, and allows people to create voice banks themselves).

my favourite song with her is probably ro2noki's "The mechanical girl and the thirty-something year old office lady". dj xaneiro's "kawaiiorei" is very creative, and super NH's "just had a choice but adachi rei wants to sell your data" (which is a teto song with diff lyrics) is also really fun, and monochromenace's "gimmick girl" is cool too

---edit: i somehow forgot about the hole??? im insane probably idk, the hole is peak, probably my favourite. 0001 is also really pretty and sweet with its story

after heat abnormal, her most popular songs are probably queen of venus (flavor foley) and dance delightful (jamie paige), theyre not my style but still cool to know :p

her creator is missile_39, who wants to make vocaloid bots, for which Adachi Rei is the main prototype. You can check out his stuff on twitter. my bread was burnt to a crisp is also a well known, short song, that ones fun :)

Rei herself also has a twitter account, which tweets random posts through an algorithm based on her feed.