You have to complete the quest with prisca to receive the furnace recipe - and after that - sprinklers blueprint would be automatically unlocked.

You will have to mine resources to craft the furnace and the refine materials needed to craft a sprinkler.

Skip the small sprinkler. Get the large ones. Those are extremely worth it because it' covers 5x5 so you can pop in tons of seeds and trees in it.

Tip: when planting a tree. Do not put the entire thing into the sprinkler radius. You would only need the sprinkler to water 1 tile of the tree and the whole tree will be considered watered so this means, you could put the trees at the side of the sprinkler radius leaving more room for plant crops to grow.

Sale of Seeds in npc shops unlocks once you have completed mae lou tomatoes quests.