Redbull haș one.

https://www.redbull.com/us-en/events/red-bull-paper-wings-wo...

https://www.cnn.com/videos/sports/2022/05/17/red-bull-paper-...

Though it doesn't look like its consistent (there was one in 2022, but nothing from May of this year).

>It would have to be an indoor competition where a machine throws the paper planes.

I bought a paper airplane launcher as one of those gag desk toys back when working in a cubicle farm. The <$5 spent was well worth the goof off slack time it gave us for a week. For a few days, people were folding all sorts of different designs. After that, it just sat there unused and unthought about. But it was fun for the ~week

I am pretty sure I have seen a video about exactly that experiment... Will see if I can find it again.

The contests exist, but they have a person throw the plane.