If you can post some screenshots showing the contents of the Sync section on the beorg Settings tab that would be great.
One thing also to check is if you:
I think the issue here is that beorg only uses its app/sandbox directory in iCloud. So the org folder is relative to the beorg folder at the root of your iCloud files. Based on your last screenshot it looks as though your org directory is in the root of your iCloud folder.
I'm hoping to extend beorg to use an arbitrary external folder at some point, at which time you could tell beorg to use an org file at the root of your iCloud folder - or from within another app.