@virtualvivi
Please keep in mind that I turned this off immediately, so I never had any files or folders going to OneDrive on my new laptop. However, Microsoft provides instructions on how to do this. I am only providing the information they made available and combining it with my pre-2006 background in computer support to try to make it easier to understand. I have not personally followed these instructions.
First, make a backup of your Electronic Arts folder (copy and paste to your desktop, a thumb drive, or an external drive). I'm not sure what this quote I emphasized below means, but I would back up before doing anything to be safe.
Choose which OneDrive folders to sync to your computer - Click here for the instructions on Microsoft's website.
Microsoft said:
If you uncheck a folder you are syncing to your computer, the folder will be removed from your computer. The folder and its contents will still be available online.
Under #4 - Choose folders:
There is a right arrow next to the Documents folder. If you click this to open the My Documents folder, you should be able to uncheck specific folders you don't want to back up to the cloud. It also says "Unselected folders will be hidden from File Explorer." I hope this means that they will be hidden from File Explorer in the OneDrive folder and NOT from File Explorer completely.
If they are hidden completely, it will take someone with more knowledge than myself to explain how to fix that issue. Sorry, I can't be of more help.
Good luck! And share if it does anything different than what I provided here in case I misunderstood anything.