Unions, intersections and negations are available in types as well and are by no means exclusive to sets. The distinguishing feature of a set vs type is that a value belongs to just one type while it can belong to several sets.
If they don’t unless you add them to “explicitly remove such a restriction”, then that means you’re making types more set-like (set-theoretic).
In strict “type theory”, it’s the latter: types don’t have unions (in the sense that set-theoretic types do). There are sum types, which are different.