Hi Cosmo,
Thank you for reporting this issue!
We looked into this issue and found that the folder is not write protected at all, but that it’s a Music Studio bug.
The next update will include a fix for this. Until then, it’s not possible to save files into folders that were created with the iOS Files app, sorry!
To summarize, the Files app can be used to organize projects into folders, but when you edit a project in Music Studio and want to save it, it can only be saved into the top level folder. You would then have to manually move the saved project into your custom folder with the Files app again.