Food for food until they are one is a pernicious myth.
I was about to post this! Babies iron levels start to drop at around six months and they need more nutrients (and especially more iron) than can be provided by milk alone. "Food is for fun" might sound catchy but it's crap, they do actually need to be getting some food in them.
No one here has had sight of the baby's red book/growth chart and the OP herself says she doesn't see them too often and certainly hasn't seen an entire day or weeks worth of meals so anyone flinging around terms like "starving", "dangerously underweight" or alluding to eating disorders is talking out of the hole in their arse.
Baby who has always been on a small side, has a drop in weight that coincides with crawling/becoming mobile, the HV is advising and monitoring the situation. So far, so normal. The HV will be monitoring the baby's growth and will make whatever referrals are necessary. OP needs to wind her neck in and butt out.
The advice to give water in the night as part of controlled crying probably came from the HV to begin with, most of the HVs here recommend it from six months onwards if/when you get to a point where you want to try it. They say that if you think the baby is waking from habit rather than actually being hungry then try offering water and cuddles in the night rather than milk. If the baby isn't eating very much in the way of solids then they recommend dropping or reducing a milk feed and giving extra solids instead.