When setting the item fade-out limit to a value other than 0, that limit is only used for the fade-out animation. After the animation is over, the items are not visible at all.
Forge 1.20.1 v6.3.5

Pushed a fix version for 1.20.1-forge and 1.21-neoforge. If anyone needs it for an inbetween version, let me know.

This also occurs on Fabric under MC 1.20.1 & other. Please post a build of v6.3.6 for it, thank you.

(Plus I'm not sure why the pickaxe and the cobblestone don't fade out at all, may be my mods)

I cannot replicate this on Fabric 1.20.1. I wonder if that other mod that causes pickaxe + cobblestone to not be fully faded out is the cause here. Are you using ImmediatelyFast? If so, you need to disable its HUD batching feature to use AutoHUD's fade.

Disabling that option or ImmediatelyFast itself got rid of random items not participating in the fade-out, but they did still disappear at its end. The "issue" turned out to be that I didn't notice the presence of the Fade-out limit for items option, which defaults to 0.0. It'd be nice if it defaulted to -1.0 instead like some other options, meaning "copy the hotbar's own transparency" in this instance. My apologies, and thanks for the quick help.

Ah I see. True, that is confusing. I will put that on my list.