Because govt. employees are union, I'm afraid you are right.
One of the most useful amendments to the Constitution would be to prohibit government unions. As it is, it's govt. employees vs. taxpayers. We always lose.
Don’t really need an amendment, just get Trump to issue an OE undoing JFK’s original OE. Then pass legislation forbidding federal employee unionization, so no future EO can re-establish it. Much better then cluttering up the Constitution.