Working with folders on the desktop is somewhat more limited in functionality on Ubuntu 19.04 than in previous versions. The reason for this is that they had to move to a different mechanism for handling files on your desktop.
Because of these limitations, you currently cannot drag and drop files from the file manager on folder icons on the desktop to copy/move them there, nor paste contents in that folder using the menu that appears after right-clicking the folder icon.
Double click the folder icon. A file manager window of the folder opens, where you now can drag or paste your files.
You can also move your files from within the file manager. You will find the files and folders on your desktop in a folder "Desktop" in your home folder.
Formerly, the file manager
nautilus also handled drawing the icons on the desktop. Gnome developpers decided to remove that feature from nautilus. To keep the functionality, Ubuntu has long shipped with an older version of nautilus that still supported the feature.
Since Ubuntu 19.04, Ubuntu ships with the latest nautilus version. To still offer desktop icons, now they use a Gnome Shell extension "Desktop Icons". This extension is still in early development and limited in features.