The same powers all capitalists use over forces of governing.

By this logic, regulatory captured is impossible because an industry is only capable of influencing under its sphere. Government being influenced by capitalism is a direct proof of capitalists influence outside of their sphere of control.

The power of the people is unity to force the wealthy to act.

The two are unrelated, just happening confidently AFAIK. That said, the purpose of a widespread strike is to make people that would normally be unaffected pay attention. Grinding the economy to a halt forces action, at least in theory.

Business ties, lobbying ability, probably things I can't think of because it's not my area of expertise.

The entire world is interconnected in one way or another, even those tribes that have sealed themselves away from modern societies are affected by climate change or even just local environmental changes. Thinking that anyone could be wholly independent from anyone else is very shortsighted thinking.

I can see how it can be potentially problematic. For example, If I’m the owner of a shipping company what leverage do I have over Hollywood execs to pay writers and actors better?

Who cares? That's the shipping company execs' problem, not the workers'. More importantly, "potentially problematic" is far below the standard necessary to justify limiting workers 1^st^ Amendment freedom of association!

Those Hollywood execs work for giant conglomerates that own a whole host of media properties including television stations. If the CEO of UPS, one of the largest, if not THE largest, shipping companies in the world, called up Viacom, for example, and said that UPS is going to pull advertising from all Viacom owned entities if they don't give into SAG-AFTRA and WGA demands, that would do enough damage to potentially end the strike. It would cost Viacom millions of dollars on top of what they're already going to lose from the strike.

But UPS isn't going to do that because if striking works for anybody, they might have to pay their workers more.