How can I automate my crop harvest?

There is no "automated" method of harvesting planted crops for replanting or to consume yourself.

You don't need to collect the food in order for your settlers to eat it.

Set up a Scavenging Station and assign a worker to it in each of the settlements you wish to collect excess scrap/food/water! You can find it under the resources > miscellaneous tab in workshop mode.

Summary

There is some automatic harvesting, but it's inconsistent and less efficient than doing it manually.

Some crops, including Corn and Mutfruit, will be automatically collected and placed in your workshop. However, you can collect more crops from a single manual harvest of your plants than will show up in your workbench, and some crops, such as Tato, don't seem to be collected automatically.

It seems that you can do both, though. Going forward, lacking more tests, I will be keeping extra crops on a follower, and pulling any extra crops out of my workshop, in addition to manually harvesting.

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Notes on Tests

I think my tests may have been messed up by supply lines, and the fact that other settlements were relying on my test farm for food. A better, future test would be with one settlement not connected to others. If anyone conducts such a test before I get to it, please let me know.

I had about a dozen each of Tato, Mutfruit, and Corn planted in Sanctuary, near the default cooking station position. I completely cleared my workshop of any crops of any type, then slept for one hour at a time, checking the workshop after each hour, for three days. I found no plants in the workshop.

I then left town and came back the next day. I found four each of corn and mutfruit in my workshop, and zero tatos. Four is a lot less than a dozen. Other times I came back I found more or less, but never as many as there were crops planted. The fluctuating amount could have been impacted by fluctuating food needs in my other settlements.

It didn't seem to matter whether I had picked the crops myself recently or not, but once again I'm concerned that my supply lines may have been contaminating my test results.

If the supply lines are responsible for crops showing up or not, I'm surprised that it was my tatos that weren't being picked, as most of the other settlements have tatos planted. Maybe the tatos in their workshops were interfering, counting as crops in the workshop?

Clearly, more, better tests are needed to figure out all the parameters, but I've done enough to determine that at least some automatic harvesting occurs, but that it is not very efficient compared to picking the plants yourself. On the upside, it seems you can do both.

Normally the settlers harvest the crop for you, but they also need to eat. If you have 5 settlers and 10 corn, they return zero to the workshop. They return the rest after they eat what they need. If you harvest yourself and use the production, they have nothing to eat and the colony satisfaction get down.

All settlers, including these connected to network eat first the tato. If you have 5 settlers in order to get tato production, you need a minimum of 11 tato plants.

Also Sanctuary seem bugged for unknow reason, and seem periodically need to be harvested manually.

It seem also that you have a food cap in workshop, after a certain amount of harvest, settlers stop storing food in workshop. You need to remove the food from the workshop and store them in another container.