You can get at least the home menu on dolphin. Either do a full NAND dump from the wii, or get a .iso of a game, right click when in dolphin, click properties, then filesystem, then partition 0, then _sys, then extract all of this folder to your iso location (or work out what file is the menu, I know it starts with an n, but that's it). Some games don't have this, but I know mariokart definitely does.
OS: Windows 10 64 bit Professional
CPU: AMD Ryzen 5900X
RAM: 16GB
GPU: Radeon Vega 56
CPU: AMD Ryzen 5900X
RAM: 16GB
GPU: Radeon Vega 56