Nintendo owns the rights to Bayonetta now, so she is just as much a first party character as Mario. Just because Nintendo pays a Developer to make a first party game doesn't make it any less of a first party game. If Platinum makes Starfox (which Kamiya wants to do) does it become second or third party?
No. Ugh. Your critical thinking needs work.
Starfox's intellectual property belongs to Nintendo. They own the ip, thats whats needed to make it first party. Just because you publish a game, or even make it, doesnt mean you own the ip.
If that were true sega would own bayonetta, and nintendo would have had to go through sega instead of p* to get bayonetta 2.
Dont bother attempting to find kamiya's tweet, I know exactly which one you misunderstood to arrive at your current position.
Nintendo owns the rights to the INDIVIDUAL GAME Bayonetta 2 because they published it.
P* owns the bayonetta ip, bayonetta 3 can appear anywhere p* wants.
Nintendo would need to buy p*, or buy the bayonetta intellectual property for bayonetta to become 1st party, in which case they can pay anybody develop the game and have it still be 1st party. Because they publish AND own the property.
But since they dont, and platinum does, its a third party exclusive.