Unions don't do solidarity strikes across the entire Nordics without having the support of the people they're trying to help.
> It is people working elsewhere -- or rather, the management of the labour unions that organize those other people.
The people you call "the management of the labour unions" are workers just like the rest. Again, they are not "career-unionists", they are workers who care about worker rights, just like all the other people at the other unions joining the strike.
How do you know this though? Union membership is anonymous. You have no reason to tell your employer you're a member. If there's a strike all employees can legally take part to help stop identification of members. Every member of Tesla could be a union member saying they aren't to avoid pushback by Tesla. That's just as likely as none of them being a member.
It is people working elsewhere -- or rather, the management of the labour unions that organize those other people.