Wii Hardware/Wi-Fi
The Wii features a Wi-Fi chipset from Broadcom, specifically the Broadcom 4318. This Wi-Fi adapter is unfortunately heavily constrained due to how it's connected, however. You may have noticed that the Wii's Wi-Fi speeds are quite lacking for a device released in 2006, and you would be correct. The Wi-Fi module is connected over Sonics Silicon Backplace (SSB), connected over SDIO, on the Hollywood chipset. Unfortunately, this was not designed with speed in mind. The overhead of TCP/IP, over 802.11 Wi-Fi, over Broadcom's Wi-Fi interface, over SSB, over the 1-bit SDIO protocol, is simply too much for the Wii's mediocre CPU to handle.
Wii-Linux has included support for the Wi-Fi chipset since at least MIKEp5 [double check?]. Upstream Linux also has drivers for all components of the Wi-Fi stack available, although they don't seem to function on the Wii. It's unsure if this is known about by the upstream maintainers, but it seems to have been broken since at least Linux 5.0.