Were you able to successfully modify the share or folder permissions using Windows File Explorer? If so that may cause problems since the My Cloud, because it uses Samba, may have problems with Shares or folders within Shares that have their file/folder permissions and owner modified outside of the My Cloud Dashboard.
In the screen capture above what is the file
.vftTestData? Never seen that before on a My Cloud.
Can you copy files into other Shares/folders outside of the Public folder? If so you may have to use SSH to access the My Cloud at the “root” level to see what the permission settings are on the Public Share and who owns the Share/folder.
For example at the SSH/root level of the My Cloud I use (first gen v4.x single bay) using WinSCP, indicates the following for the Public Share properties.