Tell us a little more about the cats (non troll)
Without getting into timeline or setting bs, I'll try to explain the main cast and some basic story stuff.
The main cast are Makoto and Matasuke (his name is likely to change tho for reasons), who are the leaders of the clan and basically own any of the businesses the clan runs, Takumi, Kurenai, Yawatama and Nami with a few others showing up here and there. Makoto also turns into a younger version of herself, who everyone calls Aotama, and outside the clan no one knows are the same person, she's just assumed to be Makoto's daughter. Luckily the rest of the bunch are easier to explain.
Takumi is a nekomata, unlike most of the cats who are bakeneko, and he has a grudge against certain people. He's basically in a contract to get rid of those folks in return for staying "alive". When he doesn't have a specific target, he just works as a body guard for the other cats but also covers other duties as needed. He's been adopted as Makoto and Matasuke's son.
Kurenai, Yawatama and Nami (along with "Aotama") are entertainers working for the clan, which has different details depending if it's the modern AU or the Edo one, but most of their time is spent working on routines, advertising to clients, putting on shows. Kurenai acts as an "older sister" to Nami, in the sense that she's the one who helps teach her various things and Nami's reputation reflects back on Kurenai.
Nami actually starts off the story as a waitress, and in modern AU it's at the clan's cat cafe. (Edo AU it's a teahouse.) She later gets chosen as an entertainer. She has two conflicting dreams and one is to be famous and well loved by the public. In Edo period, she wants to travel even knowing that if she did she could never return to Japan. In modern times I actually haven't decided what her alternate goal is since I haven't worked as much on that.
I feel I should also mention that Kurenai and Yawatama are girlfriends in both timelines. Kurenai is a bit brash, and despite being a good few decades older than Takumi has a sibling-like rivalry with him. They might fight and cause trouble but they don't let it get too rowdy, and they'd defend each other fiercely from anyone outside the clan trying shit. Yawa's more soft-spoken and polite but is good at handling difficult situations/customers.