I tried searching for recent discussion on this but couldn't find any. Is there an update or progress on making homebrew subraces and variants fall under their parent homebrew race's header?

Even something like custom race groups would be helpful.

No. The common practice currently is to name them so the group alphabetically using the following convention:

“[Race], [Subrace/Variant]”

That's horribly inconvenient and breaks the already established convention of subrace name first. I hope this is on the to do list.

I have no idea, I don’t work here, I just live here.