I'm arguing two points.
1. I'm arguing doesn't make sense is the way they talk.
"He used his coat as an umbrella."
If umbrellas aren't common, no layperson would talk or think like that. You'd be comparing common item to non-common item. Instead, in setting, it would make sense to say "He used his coat to shelter us from the rain." If a mid level craftsman with reasonable enough income to own land can't afford an umbrella, why would anyone else compare things to an object they don't have? It's equivalent to a layperson nowadays saying "He used his tent as an office building". No layperson thinks in the terms "I used my common object as a replacement for very expensive rare object."
2. Umbrellas shouldn't be uncommon
Refined enough metallurgy to create wires for "magic circuits" requires incredibly precise machining methods from post-industrial revolution technologies. Hence, it does not make sense that, along with these wires, other easy to industrialize materials (such as umbrellas) could not be manufactured. Let's even forget the industrial revolution. Umbrellas originally became common spread among noble-men using oiled canvas in the 16th century. Later on in the series, the soldiers states they wax their tents to keep water out. These umbrellas didn't use wires, but we have wires, which means, equivalent to our time. Their wire technology is 18th century, but they haven't figured out mass production of umbrellas using (insert monster/animal bone) ribbed umbrellas in the 16th century.