Turn Off Whole Line Copy in Visual Studio Code

Even after applying the "editor.emptySelectionClipboard": false setting the problem would persist. I had to remove/edit the project specific settings in the .vscode/ folder within the project folder.

In Settings enter the following line:

"editor.emptySelectionClipboard": false

That should do exactly what you want.

Because this comes up on Google as a popular answer...

FYI this is also now a setting in the Settings GUI, search the settings for "empty selection" and it'll narrow it down. Untick to disable and praise your chosen deity.