Take a look at this example:

I noticed warnings in development mode when I access the nested menuitem:

vue.runtime.esm.js:4642

testapp.zip
[Vue warn]: Property or method "__v_isRef" is not defined on the instance but referenced during render. Make sure that this property is reactive, either in the data option, or for class-based components, by initializing the property. See: https://v2.vuejs.org/v2/guide/reactivity.html#Declaring-Reactive-Properties.

found in

---> at src/menuitem/index.vue
at src/menu/index.vue
at src/menubaritem/index.vue
at src/menubar/index.vue

at src/App.vue

This warnings does not occur if I run a production build, with the below settings:
Vue.config.productionTip = false;
Vue.config.devtools = false;

I attached the project.
Can you investigate?