This coin was "stamped" in 2014 at the machine in the Rexall Drug Store located at 131 Ocean Boulevard in Hampton Beach, NH. The machine was still in service as of 8/12/2023, according to PennyCollector.com. According to this website, "Machine is working. Coin is centered press."
Link to PennyCollector.com webpage on the machine that made this design: Click Here
Attached is a photo of the obverse (with the design that was rolled onto the penny), a photo of the reverse (no rolled design, but the reverse of a normal Lincoln Memorial cent is still faintly visible), as well as a graphic of what the design is supposed to look like (courtesy of PennyCollector).
I wish I could tell you what kind of bird is pictured on this piece. My best guess is a type of shorebird like a piping plover, or just a strange rendition of a seagull. I'm not exactly sure.