Hideki Kamiya, who is the Director of PlatinumGames has detailed the process of creation for all three Bayonetta games.
The 15 tweet long Twitter thread which dropped out of nowhere has given us insight to how Bayonetta started as an Xbox 360 exclusive, going to a multiplatform game, to a Nintendo exclusive IP.
Bayonetta 1 was apparently supposed to be an Xbox 360 exclusive game before SEGA decided to port it over to PS3. Bayonetta 2 was going to be multi-platform, before SEGA put a hold on the game. Nintendo then helped fund the game (along with SEGA) and made it exclusive to the Wii U. Nintendo also fully funded the original Bayonetta to come to the Wii U.
With Bayonetta 3 (and presumably Bayonetta 1 and 2 ports), Nintendo is fully funding the game for Nintendo Switch with SEGA allowing them to use the Bayonetta IP. Without Nintendo, this game wouldn’t be able to exist.
At the time, our company had only just been established, and we weren't properly equipped for multiplatform development, so after discussing with Sega, we decided to develop the game exclusively for Xbox 360. (4/15)
When we started making Bayonetta 2, we initially received funds from Sega to develop the game for multiple platforms, but the project was halted due to circumstances at Sega. Nintendo then stepped in to continue funding the game, allowing us to finish it. (6/15)