Farmers do not harvest.
The crops in the fields are fully grown and the player can harvest them. However, the farmers do not harvest.
Farmers do not sow seeds.
The fields are tilled and have a water source. The player can sow seeds there, but the farmers do not.
Information with unclear relevance.
When trying to give crop seeds to a farmer, he does not accept them; they simply fall at his feet. This behavior is the same for adult farmers created by spawn eggs and farmers who have just grown from children into adults.
Create a new world and quickly go to a nearby village. No mods or add-ons are used at this time. The fields there only contain harvestable crops. However, the farmers do not harvest the crops.
Sounds like mobgriefing may be off for some reason, you should check that.