i discovered in play tonight the botanist's pickaxe lack the minecraft:cluster_max_harvestables tag, which causes it to harvest 2 amethyst per cluster instead of 4 as per vanilla pickaxes. i think it also keeps fortune from being able to trigger on amethyst clusters.

you possibly also want to apply the forge:tools and forge:tools/pickaxes tags for good measure, although i don't know for sure what if anything keys off of those, but it seems to be the going thing

according to jei the skyseeker pick also lacks these tags, although i didn't personally test it.