Looks like asarum italicum, invasive as well.

yes, Arum italicum. It has rhizoms which sometimes sit very deep under the surface.

Getting rid of them is tricky. After flowering the foliage will die and disappear.
If you want to have shrubs I would keep them, with taller perennial they could work as well.

They are somewhat toxic and their plant sap can cause skin irritation. So just wear gloves when pulling them out.

Not sure about invasive, they set seeds and spread by rhizomes but at a medium pace.

Bye, Lin

Here is a link that might be useful: Arum italicum