On Ubuntu 22.04 with VirtualBox 6.1.38 I noticed that for a shared clipboard I need to re-install the Oracle VM VirtualBox Extension Pack each time a new VM is created.
When I create a new VM I need to go to File → Preferences → Extensions and remove the Oracle VM VirtualBox Extension Pack and then select and install file Oracle_VM_VirtualBox_Extension_Pack-6.1.38.vbox-extpack
.
If I don't shared clipboard won't work.
BTW, drag-and-drop does always work.