The Apple icon guidelines do allow some limited deviation from the "squircle" outline, so here's one possible variation:
The more compliant thing to do would probably be to have a spiral-bound notebook with all four corners rounded to match the "squircle", but I'm being lazy about drawing a metal spiral from scratch, so this is literally just the GNOME notebook icon with the "squircle" instead of roundrect corners.
I also decided to try styling the "J" glyph as a cutout in the front cover of the notebook, which gives it a plausible reason to be 3D.
Here's a comparison with the other versions:
And here it is in the dock with some other Big Sur icons (specifically including a custom Discord icon that also violates the "squircle"):
It could probably use some finessing.
As before, this variation is available as an editable vector PSD in my pull request if you want to fiddle around with it yourself.