No. A new Banjo-Kazooie for Wii never happened and never will.
Microsoft + Nintendo relationship is strong (Minecraft, Cuphead, Ori, Sea of Thieves (PS5?), CoD parity). A **new Banjo game (Banjo-Threeie?)** would likely target **Xbox Series X|S / PC / Game Pass / potentially Switch 2** — not Wii.**