Container themes selector in toolbar

When you edit a container on a page you get a classic block toolbar with theme, font, background, border, CSS, …

Do you know if it’s possible to use the themes drowdown list to assign container variants ?

EDIT :
I found the package of the excellent JohnTheFish (Container Magic) that bring much more but I was trying to find if there are some container customisations possible by default with Concrete CMS.

EDIT 2 :
This conversation from 2021 is similar too : Changing Container values using variables

You may want to +1 this Github issue