The Steampunk route would be to use the digital system, wrap it in brass, and then add a totally separate system which belches steam, makes cogs whirr, and makes dials spin.
I’m sorry, I just have to anchor here for a moment. I am a naval aviator. I fly the F/A-18F Super Hornet and I launch and land on carriers. I have well over 1000 hours in that aircraft, and I’ve deployed multiple times to combat zones (and non-combat zones, but no one cares about peacekeeping or humanitarian missions). Now I’ve been on the Carl Vinson and the Ronald Reagan, and not the Ford or, say, the Enterprise, so I’ve maybe got a little next-generation bias going here, but let me just say, from the cockles of my America-the-beautiful heart, Fuck You.
Steam catapults are hard to maintain, dangerous and unpleasant to be around, give my enlisted dudes hives and burns and various other health issues, and oh yes, have killed aviators (destroyed multi-billion dollar aircraft, damaged the SHIP ITSELF) when they have even the slightest malfunction. The changeover to digital catapults is awesome, lifesaving, and improves the quality/duration of life for fucking everyone on the ship. When my ass is strapped to two rockets and some tiny wings in the literally pitch-black night on the uncaring ocean with hundreds of pounds worth of bombs and jet fuel tucked literally less than 12 inches away from my body, I want the thing that grabs me, punches me from 0 to 160 in 1.4 seconds, and drops me 40 feet from the surface of the inky, cold water in front of a 101,000 ton hunk of nuclear-powered metal moving at 34 knots to be the newest, smartest, most powerful machine that man has yet invented.
Baste your steam-powered good ol’ boy aesthetic in maggoty horse shit and swirl it around your pus-encrusted asshole.