It finally works...but really took a LONG time to get them to work properly
The Styles now work in Capture One 20, but the way to bring them to appear and even more to properly work took me about 10 days. I've been contacting both C1 Support as well as Earth Oliver whom I've had some great conversations before already. Only Oliver was able to help me work things out but even we needed several days to do so. It would've saved me (and presumably Earth as well) a decent amount of hours doing research or trying to get the LUTs to appear (and after that: to work!). Turns out that with Fuji GFX Files there have to be taken precautions to get them to work and also that it's simply not possible to import the LUTs via C1 right now (you need to actively copy / paste the Styles inside the hidden program-path to show up). It would've been nice if that would've been highlighted in the product. They work now, but to be honest, the way there was kind of cumbersome and could've been MUCH easier if mentioned somewhere.