I've had 0 issues running touchscreen and pen on Mint, and SAI can just run on bottles/wine, right?

https://github.com/TibixDev/sai2-guide

The solution on each distro is mostly going to be the same. Run sai in a bottle and edit the config.

Mint delivers a flatpak package of bottles, which is suboptimal, but can be fixed using https://www.virtualcuriosities.com/articles/1911/bottles-doesnt-work-on-linux-mint-because-its-a-flatpak