It is a civilian-usage imitation of a British Merchant Navy button. Navy buttons
The reason it is definitely civilian:
Uniforms which get exposed to salty air and saltwater should not use iron/steel-back buttons, which can cause rust/corrosion stains on the uniform cloth. So actual military-issue Navy uniform buttons don't have an iron/steel back.
There is an exception to that rule. In the past, US Navy kepi (hat) strap 13mm buttons sometimes had an iron/steel back, because staining doesn't show on the black leather strap.