Shouldn't the item be under
submenu_start[lumber]
--
submenu_end[lumber]?
I've never done Timber modding, so there's that.
Noy sure why you have it use HIDEWORKING vs TIMBERCRAFT or CARPENTRY?
Out of curiosity, I have to ask: you likely can harvest unlimited birch-bark from any trunk, be it birch or pine? I don't think there's UX visible tags for peeled birch trunk. Only tags for trunks, to my knowledge, are felled in rain yes/no.
Edit: just checked, the subcategory is lumber, not timber. At least that's where stakes and staff are in the diy_glossary.