[2020] New Farming / Harvesting Crops / seed system broken?!

Yes, Seeds require 5 to craft, and at most yield 3. However seeds once planted are infinitely renewable. You don't need to re-plant them every time. Once harvested, crops now return to a seed state and grow again without the player doing anything extra.

So at 3 harvested each, 2 harvests makes a second seed, 1 harvest makes a third, one harvest makes a fourth, one harvest makes a fifth and sixth, and so on.

That is certainly odd. Do you have any old mods that could be interfering? Did you properly clean the game data and re-install when updating to A19?

Is it possible you're 'overkilling' the plants? If you hit once to harvest, and inadvertently hit a second time, you'll knock out the new seedling. Like, this seems unlikely, but you'd do this if you were harvesting with an auger for some reason, with its high attack rate.

Edit: I see you said no OLD mods, not no mods. Try it with no mods. If you want it to work with mods we'll at least need to know what mods you're running.