Japanese cat lore is unusually specific about conditions. A cat that lives long enough transforms, and the ages given in Edo period writing vary but the principle does not. A cat whose tail is long enough may split it and become a nekomata, which is treated as a separate and more dangerous being than an ordinary bakeneko. Those two rules together explain a practice that outlived the belief: tails were bobbed, and the short-tailed cat became the preferred domestic animal in Japan.
The powers attributed are domestic rather than cosmic. The transformed cat walks upright, speaks, takes the shape of a household member, and above all consumes lamp oil, which is a detail that sounds arbitrary until one remembers that lamp oil was rendered from fish. The cat is not doing anything a cat would not do; it is doing it at the wrong scale.
The Edo stage turned this into an industry. Cat plays were a reliable draw in kabuki, with the transformation staged through quick costume change and trick sets, and woodblock prints of cat scenes sold on their own. By the nineteenth century the bakeneko was as much a theatrical genre as a belief, and the modern versions in film and manga descend from the stage rather than directly from the village accounts.