You don’t want union — as you said, it will create a new HashSet. Instead you can use Extend::extend:
use std::collections::HashSet;
fn main() {
let mut a: HashSet<u16> = [1, 2, 3].iter().copied().collect();
let b: HashSet<u16> = [1, 3, 7, 8, 9].iter().copied().collect();
a.extend(&b);
println!("{:?}", a); // {8, 3, 2, 1, 7, 9}
}
(Playground)
Extend::extend is also implemented for other collections, e.g. Vec. The result for Vec will differ because Vec does not honor duplicates in the same way a Set does.