That power comes from the idea that the federal employees can shut down government operations if they stop working. This administration (supposedly) wants dearly to shut down government operations, so the union doesn't have any power.
Federal employees are not permitted to strike. See 5 USC § 7311.
Federal employees are not allowed to strike
Nobody can stop them
Confidently incorrect. Federal employees marked as "mission critical" cannot strike, but other federal employees can. Unions take this into account and have workers strike on-behalf of mission critical employees.