I’ve only ever done this inside a rule…
In DFFS rules config there is a section for “Hidden headings or Elements”.
In there I’ve got .ms-toolbar
That’s the class I found by using developer tools to inspect DOM elements
(Note this is for a SP2010 site – possible other versions are different)
You could also use this same class in custom CSS to apply globally, but for us we only wanted to hide this for end users, admins still have visibility.