Is there a way to upload a folder from the Files app into a computer on the local network?

FE File Explorer can do this:

FE File Explorer is a powerful file manager app on your iPhone and iPad. It can access not only local files, but also files on your computer and NAS. Stream movies and music to your iPhone/iPad. Directly view and manage documents, photos, files on your computers and cloud without downloading to your iPhone/iPad.

1. Add the remote computer's server (I recommend a WebDAV server)
2. Now add the directories from the Files app you need
3. You can copy stuff between these "remotes" now. Take care not to background the app while the file transfers are ongoing, as iOS sucks and closes all background apps.

I achieved ~63 MB/s using this method.