The Monster Manual says this of Sprites:
Poison Brewers. In their forest domains, sprites brew toxins, unguents, antidotes, and poisons , including the sleep poison with which they coat their arrows. They venture far into the woods to harvest rare flowers, mosses, and fungi, sometimes crossing dangerous territory to do so. If desperate, sprites even steal their ingredients from the gardens of hags.
However the stat sheet doesn’t list proficiency in herbalism or alchemy. So, is the above quote just flavor text to explain the arrows, or could the Sprite familiar make other poisons (and possibly potions) as well based on the text above?
If so, I’d imagine it to work the same way as a character making poison and potion (1/2 the cost plus a certain amount of time, so that the Sprite doesn’t just become a poison factory).