I don’t know how I never realized this until just now, but “die Steuer” is “the tax”, and “das Steuer” is “the steering”, so “der Steuermann” sounds like it should mean “tax collector”, but it actually refers to the guy who steers a ship. “Tax collector” would be “der Steuereintreiber”.
Wiktionary says the two meanings are related and have their root in the same Proto-Germanic word, and for “die Steuer” it says: from Old High German stiura (“support”).
I don’t know whether it’s true or not, but I think the link between the two may be the verb “etw. beisteuern”.
It means “to contribute sth.”, but literally “steer by”, and I always have the image in my mind that you steer something in someone’s or a project’s direction as support.