And now that enough time has lapsed and enough responses have been posted…
Spare 4-pack of TP.
Seems perfectly sized for an electric toothbrush. Maybe the previous owner didn’t like having something that was always plugged in sitting on the vanity, so he had the existing outlet next to the vanity split to also feed into the niche. Also since it’s the main “wet wall” in the bathroom where the plumbing is (especially the plumbing vent stack for the toilet) it’s much more likely to be framed with 2x6 lumber. So the niche can be 6" deep if the back of the niche is also the backside of the drywall in the next room.