I think this is the central point. You can do all those things, but are you entitled to use company equipment to do so?
The term spying becomes less clear-cut in that context too. It's spying if I get your personal private communication, but monitoring one's own internal network would not normally be considered spying.
The other prong of this that is still possibly illegal though is spying on union-specific activity, and leaving that information out for employees to find, which fits under the criteria of making employees believe they’ll be spied on for unionizing - even not on company IT systems.
There’s already an NLRA complaint against amazon (source: Matt Bruenig on Twitter) over the Union-spy job posting. It’ll be interesting to see where that goes and if this gets tacked on.