Is the Border Patrol Union Illegal?

The Border Patrol Union is fairly terrible. Jenn Budd has documented extensively their awfulness in many different contexts. But since in 2020 Trump designated CBP as a security agency, the union might actually be existing outside of the law.
I again want to thank Jenn Budd for bringing this point to my attention. 5 USC 7112(b)6 says in relevant part