A union is recognized by the NLRB and has certain statutory entitlements regarding strikes and the ability for employers to fire striking workers. "Labor movements," writ large, do not require those statutory entitlements. Modern unions can be understood in terms of their ability to collectively bargain without fear of direct reprisal in terms of employment. Otherwise, collective bargaining has always been an option (it's just humans acting in concert), and long predated the concept of "unions."

I feel confident that most people would say a formal organization of workers that engaged in collective bargaining and strikes without legal protections was a union, even if it existed before the NLRB. If what you really want to talk about is "modern legally-recognized unions" then just say that.

Maybe, but when they say union membership is down, they mean NLRB recognized unions. We do not have good stats on labor movements writ large. To the OP’s post, Google’s not tackling a labor movement. They’re tackling “unions” with statutory privileges.

So you would call a labor party a worker union? Labor seems to be able to organize just fine regardless if there are unions or not, as long as they are allowed to vote.

If it's a party composed of workers and it advocates specifically on behalf of the interests of the members, then yes I would call it a union. If party membership is open to anyone and labor issues are only some of the planks in its platform, then no I would not call it a union.

Honestly I think this is just continuing a very uninteresting semantics discussion - now we have to decide what "labor party" means. The point here is that you seem to have a different definition of "union" than the average person, which is fine, you should just be aware of that and watch out for misunderstandings when you're discussing with someone so you aren't talking past each other.