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Do workers keep working when I'm far away?

Herdwarden, Seedsower and Grovetender shrines and Runekeepers do, by default. Whoever hosts the world loads each one's area (its buildings, plants, animals and spirits, never wild creatures or spawners) and runs it as if a player stood there. In single player that's your own game. The setting is KeepFarmsCropsTreesAndGeneralsWorking in BepInEx/config/com.yohanb.runebourne.cfg; turn it off if a server with many bases lags.