For those with a modded Wii U console, you can now integrate your console into Home Assistant via a mod called "Ristretto", with massive thanks to @warm frigate and the rest of the Nintendo/Wii community who have provided the core development, assistance, support and testing just making this possible.
Currently you are not able to turn on the console remotely as the hardware itself doesn't support things like WOL etc, however the integration does expose a "Request to turn on" trigger much like the Web OS TV integration does allowing you to put a fingerbot on the front of the console.
You can find the Wii U integration and all the necessary instructions here: - https://github.com/wiiu-smarthome/ha-wiiu/
You can also find Ristretto here - https://github.com/wiiu-smarthome/Ristretto