Sorry to have to say, that button-front is not from a civil war US Army cape-pin/poncho-clasp. Apparently, all of that item were made by the same company, using the same button-front. The design of the eagle and shield on Fishbone3d's button-front is not the same as what is on the cape-pin/poncho-clasp.
Speaking of which... the "iron-backed eagle button" at the Civil War Outpost website is not a button ...it is a cape-pin/poncho-clasp whose long iron shank rusted away.
"Coatsize" iron-backed eagle buttons are very-very rare. But I've dug a few cuff/kepi-size ones. Fishbone3d, please make and post a "sideview" photo of your find, so we can see whether it has a low-convex or high-convex dome. Also, an exact measurement of it would be helpful.
Usually, on civil war era US Army "eagle buttons," the eagle's body (except for the head and neck) is bilaterally symmetrical ...meaning, the shape and angle of each wing and leg is a mirror-opposite of the other. That is not the case on Fishbone3d's button-front. In particular, note that the legs are in somewhat different positions from each other, relative to the shield. Also, the gap between the neck and wings is not the same on the right as on the left. That's very unusual for an 1854-to-1875 US Army eagle-button. And I'm about as sure as I can be that it is not a pre-1854 nor post-1875 US Army Regulation eagle-button.