I’ve seen this issue around, and finally sorted it out. If you’re leveling a fresh gatherer, or your alt with mining didn’t quite catch all the weekly knowledge for past weeks, this might be helpful.
Note that this ONLY applies if you’re in a knowledge “catchup” state for mining (i.e. you’re behind the curve by some amount due to not obtaining prior weekly knowledge). I’m not sure how far catchup goes (I’d assume you can catch up knowledge for missed slabs/erosion-polished but not past weeklies).
If you aren’t finding null slivers, I’ve tested and it appears that they only drop AFTER you exhaust all weekly sources of mining knowledge. This includes the weekly quest, which at the moment is 2 null stones and some bismuth.
Source: I tested it when I leveled my second gatherer by mining a lot before turning in the weekly. I also tested it on an alt who I was acuity shuffling on. For both, null slivers only began dropping after I burned null stones on the weekly. Yay.
Edit: For herbalism - I didn’t specifically test it because the weekly knowledge quest isn’t costly for herbalism, but I’d assume this also applies to deepgrove roots.