Yakuake has only one instance over all of KDE plasma desktop activities. I think it will be a welcome feature that it has different instances for different desktop activities, like other KDE applications (Dolphin, Konversation, etc.).
Note: this feature is controlled by clicking on the icon of the KDE app in the titlebar of the mainwindow. Since yakuake's titlebar is a bit different (it is at the bottom of yakuake instead of on the top), a way to implement it would be to make the (blue terminal) icon of yakuake clickable.

Reproducible: Always