Villagers not farming?

So I’m trying to make the fully auto crop farm. I have tested carrots and they seem to work fine – the villager farmer throws carrots at the villager and the hopper minecarts collect it.

However, wheat does not work. I know they can make bread with the wheat and throw the wheat but after giving the farmer stacks of wheat, they don’t throw wheat or bread during their non working time.

So is there any other way to make fully automated farm? I need a lot of wheat to sell it on the servers I’m playing. But I don’t want to like farm it by hand as it takes a lot of time and it’s super annoying.