VirtualBox shared clipboard does not work

You should install virtualbox-guest-x11 package as dkms installs only the drivers. Then run the command VBoxClient --clipboard.

Sources How to fix virtualbox's copy and paste to host-machine?

The method with 'VBoxClient --clipboard' did not work for me.

So, I downgraded VirtualBox from verison 6.1.4 to 6.1.2 and the problem disappeared.