Bayonetta's shadow is not of herself, but of the demon Madama Butterfly, who she made a pact with and is the source of her attacks. This is most likely a reference to Devil May Cry, where Dante's costume while playing on The Legendary Dark Knight mode, which is of the demon Sparda's human form, casts the shadow of Sparda's demon form when not in Devil Trigger mode.
Contributed by MehDeletingLater
Exclusive only to the Wii U and Nintendo Switch ports of the first two games in the series, several costumes were added that are based on Nintendo characters with additional features tied to them:

•Both the Mushroom Kingdom Princess and Sarasaland Princess costumes resemble the princesses Peach and Daisy from the Mario series, with Mario and Luigi charms attached to their dresses respectively. Coins will drop instead of Halos once enemies are defeated and collecting them will play the coin sound effect from the series. Attacks that summon Madama Butterfly are now replaced with Bowser's hands and feet.

•The Hero of Hyrule costume resembles Link from The Legend of Zelda series. Equipping the Shuraba with this costume will turn the current weapon into the Master Sword. Wearing the costume replaces the Halos with Rupees as well as the standard sound effects with those from The Legend of Zelda: A Link to the Past, specifically because it is series director Hideki Kamiya's favorite Zelda game. If Jeanne wears the costume, sound effects from the The Legend of Zelda can be heard instead.

•The Galactic Bounty Hunter costume resembles Samus Aran from the Metroid series. Samus's blaster cannon can be used without needing to equip a weapon skill. Furthermore, Samus' visor works differently between the two games.

•The Star Mercenary costume exclusive to Bayonetta 2 resembles Fox McCloud from the Star Fox series. Equipping the Love is Blue/All 4 One with this costume will turn the current weapon into Arwing Guns, each having charms that resemble Fox, Falco, Peppy, and Slippy. If Bayonetta dons the costume, sound effects will be replaced with those from Star Fox 64. However, if Jeanne dons the costume, sound effects from Star Fox will be heard instead.

•The Chain Chomp foot weapon, also exclusive to Bayonetta 2, can be obtained by completing all chapters on Hard difficulty. The Super Mario 64 Golden LP can be given to Rodin and he will give Bayonetta the Chain Chomp, which plays sound effects from that game. Upon performing the Umbran Dance with either Bayonetta or Jeanne will give them Mario and Luigi's caps with both letters replaced with the letter B and J, while also having fake mustaches.
Contributed by Tuli0hWut
Hideki Kamiya has stated that he would like to develop a Bayonetta spin-off game starring Jeanne for the Nintendo 3DS.

"Given the chance, I’d like to make a game based on Jeanne from Bayonetta. Something that’s not as big in scale. Something that’s portable, that you could play in quick sessions, where she’s a history teacher and the kind of fun things that could come out of a scenario like that.”
Contributed by CLXcool
Bayonetta was going to be included in the Sega crossover kart-racing game Sonic & All-Stars Racing Transformed as a playable character, but according to a forum post from the developers, she was scrapped because the developers had trouble trying to keep her in-character without the ESRB/PEGI rating potentially going up.
Contributed by DrakeVagabond