The bluetooth devices settings page will see all sorts of bluetooth devices when those are in pairing mode, even ones that it doesn’t support; the listing alone is not enough. Apple TV system software (tvOS) will need to have the “driver” software for it incorporated, for controllers to be supported.
As the Wii Remote was discontinued in 2017, its use and prevalence are diminishing, and I don’t expect it to ever be supported on Apple TV after so much time has passed. Instead new popular controllers may get added in the future.
Connect a wireless game controller to your Apple device - Apple Support
About Apple TV 4K and Apple TV HD software updates - Apple Support