ChipInMonth

Sorry, Jet, but something being "in-vogue" has nothing to do with it. And yes, it is used in creating physical parts by a lot more companies than just Apple. It's called a C3 curve in manufacturing and CAD and it's used to create corners that smoothly transition from one surface to another. If you don't see the benefit, please ignore the post.
When something comes along that is clearly better, it should be embraced, in my opinion. This has nothing with a single implementation of "squircles". It's about ALL rounding algorithms in general as I said in my original post. Apple simply uses it in their graphics because it mirrors their manufacturing processes, and they (and I) think it looks better. If it was used by default, it would more likely adopted across the board and we could stop using the old (hideous) curves.
 

Yes, it's been in Sketch for a while already:
This is similar to Apple surface finishing for real products. It might seem like a small thing, but visually it makes a difference.

Should be the default in my opinion, but Affinity really needs to add this functionality into the rounded rectangle tool and any other rounding algorithms.
 
Short answer: "Squircles" are what make Apple products have "more than rounded" corners.
 
Great article here:
https://hackernoon.com/apples-icons-have-that-shape-for-a-very-good-reason-720d4e7c8a14

Pixelmator has implemented smooth corners. It's a pity Serif didn't get around to it. I still prefer and spend most of my creative time with Affinity products, but I find myself dipping into Pixelmator for some things. https://www.pixelmator.com/blog/2022/11/02/pixelmator-pro-3-1-adds-support-for-macos-13-avif-images-introduces-smooth-corner-styles-and-more/