Nintendo's calling the shots. They own the trademark to Astral Chain, they're pouring money into development and marketing. It doesn't matter if Platinum is owned by Nintendo or not, the development team answers to them for this title.
Bayonetta is a bit trickier. Sega owns the Bayonetta trademark, but Nintendo owns the rights Bayonetta 2 and 3 under the license of Sega.
I've always considered that 2nd party. But it doesn't really matter. For me 1st party is Nintendo developed.