See also: https://dict.leo.org/cgi-bin/dict/archiv.cgi?...
I would say "staff" is singular and means "a body of persons employed in a business" [Fowler's]. The plural is "staffs", which refers to several such bodies. Staff does not mean "Mitarbeiter" (sing.). It is more like "Personal". It is not a word, like "sheep", that has the same form for singular and plural.
However, it is more complicated than that, because it is a collective noun (like "crew") and can, therefore, take a plural verb (at least in British English).
To make it even more complicated it can sometimes be used like an uncountable noun, without an article ("You can't get staff", "by staff", "members of staff").
In your example, think of "all" as meaning "gesamt" rather than "alle".