Assuming I place a water block away from any village, and I put a composter and a villager above the water block and plant crops all around it, what is the radius of crops that the farmer will tend to on Java edition 1.14.4?
The farmer with inventory filled with carrots and potatoes got a composter in the middle of fully grown wheat field; random tick speed set to zero so that he wouldn't harvest the carrots and potatoes. Afterwards, the game has been tick-warped for 72 hours equivalent - in the latter half the villager would no longer replant anything. Afterwards, I added the diorite blocks to help measure the distance.
This is the pattern produced:
So, the harvested area is approximately a diamond with taxicab distance radius of 9.
According to the Minecraft wiki, a farmer villager will only seek farmland 9 blocks away in the X and Z coordinates, and up to 1 block away in the Z coordinates. Farmer villagers will only tend to crops inside their village boundary unless they are far enough from a village, in which they will cater to any crops.