The gamecube can't run wii games, it doesn't have enough memory.
Yes, the Switch will likely use Nvidia's next Tegra chip, which sounds like a 768 Cuda core Ampere chip on 7nm+. That is likely launching next FY.
I'm probably thinking of some dev units that were used before the wii was in its final stages of development, I know at one point modded Gamecube devkits were being used to develop some wii games (I think Metroid Prime 3 was one of the ones we know for sure)