I want to connect my Xbox One S controller to my Wii U wirelessly without having to connect it to a PC, maybe using the controller's built-in bluetooth, is there a way to do this? I was thinking of getting the 8bitdo Wireless adapter, but I don't know if it is compatible with the Wii U and I can't seem to find any information about this.
You will definitely need some sort of device to translate the commands, as the Xbox controller isn't a standard HID controller that HID-to-Vpad would be able to talk to. I don't know of any device that is *designed* specifically to do what you want.
Buy one and try it, return it if it doesn't work for you?:
You might have some success with the Mayflash Magic-NS, making the controller appear to the Wii U as a controller supported by HID-to-Vpad. The 8bitdo one might work similarly. There are also cheaper ones like the Coov N100 meant for using other controllers on Switch that might work.
Working solutions that aren't quite what you were hoping for:
You could use the controller wirelessly with the Network Client with a computer. Or you could use it wired with e.g. a Brook Super Converter to make it show up as a Wii U Pro Controller (even though AFAIK a real Pro Controller can only connect wirelessly : p) - this is what I use.