Someone posted this on Imgur:
https://i.imgur.com/zPh341R.mp4
I don't know how to make MP4s or GIFVs work here and they did not link the source.
Have a low-quality GIF!
No no no, that isn't animated and not only did the poser not pose a source, but the square video is 9x16 for no reason!
I couldn't find another version, so I used Vance to enlarge (and enhance) and cropped it:

Of course, the forums shrank it.
So, it shows the squircle rotating inside the square, shows a laser cutting flutes in each side, slightly beveling the tip, and shows it being attached to a shaft and drilled into wood, leaving... a squarer squircle.
This isn't the source, but it is similar:
One or two people shared this:
Is that the same concept? I don't know, he never once mentioned "Squircle!"
Of course, once they made the flutes it wasn't a squircle anymore, it is a 3-sided drill bit--in a square collar, which doesn't wear out?
Of course, even I knew about mortise bits!
I just didn't know their name, but that was the first result when I searched for "How to drill a square hole."
Edit! Two of those don't show up here, so I am trying to find something similar--and hoping they show up here.
This guy tries to make his own bit, which wasn't perfect, and he said said he could improve it further:
He talks kind of funny, so I needed to read the subtitles. This guy used $20,000 worth of equipment to cut a slot in a rod, pin a piece to close in the open side, and then trim it down to have a square hole.
Should I have specified wood?
I don't even understand. He milled a tapered square end, which put corners on a round hole?!
Also, he has a special machine that looks like a scroll saw with a square file instead of a blade.
This guy showed how to file by hand, use a machine he made, a mill to make a squircle, and then he makes a tapered square end like Tony, but tempers it, grinds a concave face, and uses it to chip away at corners of a round hole. Then he uses a bunch of equipment to put corners on a round hole:
this is AvE, but before he was cool?
This one seems like it requires the least expensive equipment, he put a square file in an arbor press and squared a round hole:
https://youtu.be/wpD_3UJXzSI?t=27 Are vastly more people putting square holes in metal than in wood?!
