My use of the term "steam punk" meant an impossible technology. For example, a steam punk robot might clunk around like animated medieval armor, but the "tyranny of numbers
" would make it impossible. The mechanisms to make it move might be designed, but control would be impossible. (I always laugh when I see the massive relays clicking in Robbie's face in FORBIDDEN PLANET.)
Regarding the show itself, setting aside the FJ artwork, STAR TREK went in both directions. The dialog would have primitive talk of tapes for data storage, but then Scotty would say "Bulky, solid, I think they used to call 'em transistor units." My father, a radio technician in his day, laughed out loud at that line. But the use of tapes, that seemed fine, because what else could they use?
The communicators had what we call voice dialing: when he's done talking to the ship, Kirk simply says "Kirk to Spock"-- and Spock's communicator beeps. That was so far out, so wildly advanced in the early '70s, that I couldn't come up with technical doubletalk to explain it. I thought there was no way to do that. It didn't even occur to me that a little communicator could also be a powerful computer. Like, that will never happen. (I'm old enough to still think it's remarkable.)
But as Metryq said, Mr Norman (and the Bridge machiney, when they opened a panel down by the floor) had mid-20th century circuit boards. The ship's computers made a chattering noise, created on an electric typewriter, to simulate relays. They were playing to public expectations sometimes, to lend a sense of substance to the setting.
The show had no idea how, but they just had faith that future machinery would be vastly superior. And today we have microprocessors, fiber-optic cables, rare-earth-alloy magnets, and fractal antennas that have literally re-made the world.