Just a flat button, with a broken shank. That has a hole punched through it for some reason.
Not sure on the size, even though it's sitting on a pack of smokes, it doesn't give most an actual size.
There's not going to be any definitive answer to your queries.
I agree it's a common flat button I've found hundreds over the years. go look some more they are often found in groups .
here's a chart you can save that helps date these buttons. yours looks like sample G to me.
You need to help us by measuring your items, or placing some common object, like a penny, etc., next to the object.
I would keep detecting that area & dig everything . One time I found a small railroad uniform button. I kept searching the area & dug up ALL the buttons to the jacket, that was rotted away, except for a small patch of cloth on one of the buttons. I donated the set of buttons to the small museum of the small, historical town I was in.