What tasks do you always assign in every settlement? Food seems to be the only yes for me, but even that depends (see below). What about water, defense, etc.?

I have settlements that are producing enough food but AFAIK never had anyone assigned. I'm not sure if I should be worrying about this or not. I've never tried assigning water, because there doesn't seem to be a need. For defense, I just build turrets, though I know that the defense rating increases if you assign settlers.

Also, anyone producing purified water with the treatment plant? Does that require an assigned settler?

You don't need to assign water. You have to assign settlers to guard posts if you want them to count to your defense rating. Settlers auto assign themselves to food, but only to cower minimum need of the settlement. If you want them to produce surplus, you have to assign them manually. You don't need to assign every plant individually, just one. Settler will then start working at all available, unassigned plants up to limit of 6 food (most plants count as 0.5 food but some as 1 food like mutfruit). Therefore one settler can work maximum of between 6-12 plants.

Every other structure you build have to be assigned if it says so in description in building mode. Structures which lacks assigned settlers or some resource, will show it in red instead of green when highlighting them in build mode.

Great info. Thanks for your reply.