The green piece with the jagged edge on top appears to fit with the jagged edge in the second photo, part of the same circuit board upside down. From the ruler, the whole intact board would appear to have been about 4 cm by 4 cm.
Well, I’m pretty sure they are two different colors, which would mean two separate pcbs.
Green is by far the most common pcb color, but there are lots of blue ones as well.
that is a capacitor, not a battery