Here back to report that I fixed my issue by installing mo2 with the modorganizer2-linux-installer instead of using steamtinkerlaunch, which I used in the non-working setup. I used the Modding Skyrim SE on Linux - A Headache Minimization Guide, and adapted it to my setup.
I installed "dotnet-runtime" natively on linux via package manager. Because I use Arch (btw), the extra repository provided version 7.0.11.sdk111-1. I also installed the Visual Studio 2015-2022 redistributables into my user's wine prefix ~/.wine by running the installer, not winetricks.
Now dyndolod runs ok, except for the middle part of the window being "blank" in expert mode. I think there is supposed to be a list of rules/items there. You can barely work around this by clicking the on the items to see a quick flash of the name of the list item.
I'm not sure my original issue was because of steamtinkerlaunch, could've been that I messed up my game prefix at some point.