I know right? Perfect song as sung by a legend. Honestly, regardless of who sings the theme songs for Bayonetta 3, they could never.
I know what you're saying when you say "Gaga when not Gaga," but as a card-carrying little monster, my point was that even when she's not doing the pop music maximalism she's known for, she's still very much "doing Gaga." She may be known for the spectacle, but even when she's singing jazz with Tony Bennett, she's still fully Gaga. Meat dress Gaga and piano ballad Gaga are two sides of the same coin, essentially, since she very much believes both are valid artistic expressions and manifestations of herself. But that being said, if you're more into artists like Lana (who I do like, but is most definitely a different beast), I can see why you've sorted the various Gaga modes into ultra-spectacle "Gaga" and more normal "non-Gaga." Honestly, this is just my excuse to geek about Gaga on a game site, lol.
Oddly, there doesn't seem to be as much vitriol for Switch exclusives as there were for Wii U exclusives. Probably because people are actually buying the Switch, haha. Gaga singing for Bayonetta, or any game for that matter, would definitely be a huge get. The only comparable example I could think of would be Florence + the Machine doing the theme songs for Final Fantasy XV, but much as I adore Florence, she doesn't have quite the same amount of clout. At this point, though, I don't care who sings so long as we can just get more Bayonetta 3 info!!