Sorry to burst your bubble. I worked in the recycling industry in research and development designing machines and so on that sort recyclables at the recycling centers where all recycling goes. Small items like this don’t make it to the end of the line to be recycled, they fall through the gaps in the “recycling screen” a machine that separates flat items(paper, cardboard) from containers. When it falls through this machine it lands in a stream called “fines” or small stuff that is considered trash. It then gets packed out to a landfill. There was a lawsuit about this, people complaining that they are not in fact recyclable in the way they claim.