I haven't tried myself but you're in Workshop mode when you try to set him to farm or scavenge etc?

There is a mod that makes the player unable to harvest food from plants and completely have to relie on the settlers to fill the workshop with veggies.

So, yes the settlers fill your workshop with pretty much everything that settlement produces that is not consumed by the people.

I'm always building on my settlements quite heavily and the darn slaves cant keep up with production costs >< dang it get back to work Codsworth!

Did you spoke to him after finishing quest in Concord? You can't assign him until he becomes available as a companion for which to happen, you have to speak to him.

ive never had veges added to my workbench? in fact....

sanctuary 19 settlers (not sure how as my cha is 6??) 24 food and not only does no food get added but it disappears as does any food i find in world and put in work bench, same goes for purified water any i put in disappear and any added by water purifiers disappear.

i built a cooler next to workbench and store all food (excluding creature meat, they dont seem to touch that) and purified water (once again they dont touch dirty water)

all my other settlements that have settlers in them tenpines, abernathy farm, outpost zimonja, hangmans alley, greygarden, oberland station also dont add any veges to the workbench despite abernathy and greygarden producing waaaaaaaaaaaaaaaay more food than settlers.

in all these settlements i dont have veges or water disappearing out of workbench either?

i dont have purifiers at any of these as they dont have access to any water tiles.

i also cannot assign codsworth to anything

he comes up with the command and the assign option comes up but if say i click on a group of food only the one i click on is assigned i have to manually click on command then go click on assign and do that for every single plant, but when i leave and come back anything i assigned him to is un-assigned again?

edit: he is available as a companion

I think scavenging benches also yield more "rare" materials on top of more material in general (than unassigned settlers). I remember reading it somewhere so dont take my word for it.