As @slickJujitsu said, make sure to set everything up using Docker containers going forward, it makes stuff like this completely painless.
As for your *aars, pretty sure all you have to do is create and export/download a backup in the web GUI, all your stuff including file history, settings, and stuff should follow. Check the documentation for each tool to verify before you do anything destructive though, it’s been a little while since I had to change hardware without everything being Dockerized.
For Plex, read them follow this guide step by step. It’s not generally that painful of a process. I’m assuming your pirated media is not saved locally on the Windows machine, and is on a NAS, in the cloud, or on external drives? If so there’s nothing destructive about copying files and standing up a new instance, so just follow the guide and don’t delete anything from the Windows PMS instance until you’re done setting up the new Dockerized PMS on Linux. That also goes for the *aar services.
Once everything’s Dockerized every time you update you’re effectively migrating servers, the Docker image is meant to be ephemeral. All the config folders, temp folders, media folders, log folders, etc., are mapped to permanent folders on the host that can just be attached to whatever new host you want to use.
One thing I will add is don’t map specific media library folders to your PMS Docker image, like /movies, /tv, /music, etc. Instead, make an inclusive /media folder, nest the Library folders in there, then pass that inclusive /media folder to the PMS Docker image. This way you don’t have to edit your compose yaml file each time you want to add a new Library, you just create the new folder, add the content, and map the Library in the PMS GUI.