I assume Oda, at this point, will explain that BM and Kaido have been using awakening throughout Wano. It isn't something I wanted to be true either, but maybe with how long they've used their powers, it may just be so casually incorporated into their moveset that they don't feel the need to explain it to anyone.
Like for Kid/Law/Luffy, it was pointed out because they end up consuming massive amounts of energy to use it, because they are inexperienced.
But imagine if Oda just didn't say anything about Doflamingo, Kata, Law or Kid's awakenings, you probably would just assume they either didn't have it or that their awakenings are just tied to their strongest moves.
Idk, I'm more confident he shows or explains it other villains, but we'll see. It'll never not be weird how he didn't at least point it out with these 2.