If you go to any libertarian space online or in person, the stance on private sector unions is mixed at best. The idea that libertarians universally support the strengthening of private sector unions is another strawman lie for you to feel better about your dumb ideology.
Elizabeth Warren is literally calls all of her reforms a better form of capitalism, a plan to save capitalism says she loves capitalism and your side of the aisle calls her socialist.
You can't do the Scandinavian model without high taxes and strong unions, which is why progressive activists know you can't get shyt done until you repeal Taft-Hartley. pushing for full scandinavian without a repeal of Taft- Hartley is folly.
Strengthening private sector unions, is a cost any libertarian that isn’t a purest(of which there are few) would pay to remove/drastically reduce federal intervention into the worker-employee contract.
A union set, industry specific wage > a blanket federally mandated wage.
... and I wish progressives pushed towards making it a reality.

Warren wants to put workers on corporate boards, which is as close to workers owning the means of production as it gets in this country.
Her socialist title is earned in my opinion.
If she believes she loves capitalism she has no grasp of how it works.
Imagine a corporation trying to figure how to deal with/negotiate with a union with a union member in the room