After tidying up the store with enthusiasm, I was finally able to take a photo of the Bridgestone One Touch Picnica.
It's not super compact, but the gimmick of being able to fold it just by gripping the bar above the red reflector is great.
It wasn't in the best condition, but the tires and grips were replaced with new ones. The metal and plastic parts were polished to a fine finish. It's belt-driven, so it doesn't need oiling, and it's durable and quiet. Definitely worth it for daily transportation.
BRIDGESTONE One-Touch Picnic