Games where the protagonist is a doll

I recently came across the game Ichima-san. It's a pretty weird and sometimes awkward game, but it was kind of funny. It's best to watch the trailer to get a sense of what it's about. Of similar things, I remember a fairly old game about a man made of sugar cubes. And Supraland, but that probably doesn't apply; the protagonist there is an ordinary character from their "world."

I'd like to know what games there are where the main character is a doll or a cogwork doll, but in a way that affects the plot or gameplay.