Underwonder, your find is definitely an ironbacked civilian "Fashion" button, loosely imitating the actual US Navy button. Note that your eagle's wings have very round tops... and the rope-border does not pass through the ring on the anchor's top, as it does on the actual USN button. Also, the civilian-usage imitation's emblem detail (sharpness) is very weak in comparison to the USN button's superbly crisp detail. See the photo below, showing a civil war era actual US Navy uniform button.
Lastly, I mentioned your Fashion button having an iron bac (which has mostly corroded away. Actual US Navy buttons NEVER have an iron/steel back, because the iron would eventually get rusty, from saltwater air, and washing, which would make rust-stains on the uniform. The only exception to that rule is a small USN button made for use on a kepi-hat's leather strap.
I'm including the final photo below to show y'all another variation of civilian "Fashion" imitation US Navy buttons. Again, note the rounded-top wings, and weak detail in the emblem. In comparison, on the sharply-detailed actual US Navy button you can even see vanes in the individual feathers on the eagle's chest.