This is an accepted solution.
Indeed, there is a write_files permission in the GraphQL Admin API - the documentation for the fileCreate fileDelete and fileUpdate mutations can be found here. Hope that helps - thanks!
So for files create, you can add Media like Images for example, first you'd have to action the stageduploadscreate mutation(docs).
You'd receive a "resourceUrl" returned in response from the stagedUploadsCreateMutation.
Then you'd pass that"resourceUrl" into the originalSource input mentioned in the FileCreate docs(here) and the files should be uploaded to the Files page in the Shopify Admin. Ensure your app has write files permissions too