Even more interestingly, why would they have a Sea-based Navy at all? If you have a limited pool of resources to make an army with, why would you limit some of your force to naval engagements? Considering most of the factions will be waging ground wars, and will have to deal with difficult terrain (thinking The Wastes, here) it would make sense to put your resources into airships, and be able to attack any threat anywhere.
Also, we have to take into account that where we are in the timeline is at least a hundred years after Gabriel, meaning airships have been around for a while now. This leaves enough time for true Navies to be phased out, and simple fishing and immigrant convoys being all that remain. That, and we know the environment got messed up to high heaven- how the heck is there a warship in the middle of Duel at Dawn and in Dunes? It's clear the sea level must've dropped considerably, leaving many ships hung and dry. Factoring in all the environmental difficulties airships are the most sensible and easiest method of transport.
So, in terms of lore, humanity was at a WW1 stage- we had dreadnoughts, tanks and guns, verging on aerial combat. However, a catastrophic event caused a massacre of the human population. As this technology was ground breaking (and induced by an arms race) it was confined to a group of individuals, be that scientists and manufacturers. Due to the event, however, they were killed and the knowledge died with them. The reason why they held on to some technology is some people survived- say for example we had a similar event happen now. We'd retain knowledge we were taught, say if your profession was a doctor, but you wouldn't have a clue how to rebuild a car, let alone how to salvage parts from it. This is how they have partial knowledge and a disparity in technology. Some groups would've had completely different skill sets, we're still pre-Gabriel here.
Anyway, ignoring my massive tangent, there probably wasn't a proper fighting navy, simply a couple city-states defending themselves. Once air travel was perfected Empires became an option.