universal-pidff is working on support for many wheels. I believe they are also working on upstreaming.

Thrustmaster hid-tmff2 is a module that supports some common belt drive wheels. (I had a t300 but upgraded, see below)

OpenFFBoard is fully supported without any extra drivers/modules in Linux. Even the configurator is just python+qt and works fine (This is the wheel I use).

Running the drivers in wine won't work, or at least there is no benifit that I've seen. Oversteer provides some udev rules which improve logitech support, you should install that and reboot even if you don't plan to use it. The udev rules initialize the wheel correctly, set permissions on the sysfs components, etc. AFAIK the Logitech Driving Force GT is fully supported by the in-tree logitec driver link. Can you post more details about the issues you are having, maybe with screenshots?

EDIT: I forgot that oversteer recommends using new-lg4ff for most logi wheels. So definitely give that a try as others said.

Lastly there's sim community https://infosec.pub/c/diysimulators@discuss.tchncs.de (the creator of openffboard is the mod of that community) if you're interested. It doesn't see that much action but there's a little here and there.