How much Lumin Amber is needed to unlock Nurture?

The 30 is a collection target before it is a payment. You gather the Amber out in the world, then hand the full stack over at the branch, so there is no partial progress to chip away at and nothing happens until you have all 30 in one go. Plan a trip around it rather than expecting it to trickle in.

The branch is worth learning as a hub while you are there. It is also where you upgrade the region's bloom, and that upgrade path is what opens weather control, with Prismana's weather becoming available once the bloom graph hits 60 percent completion. Nurture is the first thing you do at that counter, not the last.

One small thing that trips people up when they go looking: the item turns up as both Lumin Amber and Lumen Amber. Same item, same 30.

Not settled: Nurture is unlocked one region at a time, and whether a second region asks for its own 30 Lumin Amber is not settled.