Environment

Vuetify Version: 3.6.9
Vue Version: 3.4.27
Browsers: Chrome 125.0.0.0
OS: Windows 10

Steps to reproduce

1. Create a VTreeview node.
2. Make the VTreeview activatable
3. Add a template using the append or prepend slots
4. In the template, insert a node

The node will not be visible in parent nodes on the tree. It will be visible for child nodes.

Expected Behavior

The nodes append and prepend to parent nodes in the tree.

Actual Behavior

The nodes do not append or prepend to parent nodes in the tree.

Reproduction Link

https://play.vuetifyjs.com/#...

Other comments

Note, using selected instead of activatable works fine. Using neither selected nor activatable also works fine.