When has my backup finished?

This is not a core Home Assistant addon. The forum feature request category is for core Home Assistant integration / addons. The developer has indicated on their github repository that suggestions can be made here:

EDIT: @ianadd also there seems to be some evidence that this addon has been abandoned. You might be better off choosing a different automatic backup option. I use the SAMBA backup addon and this does have notifications of start/completion/error.