Where did you read that putting vitamins in water doesn't work because we don't know if the bird will drink enough? I have been keeping birds [and putting vitamins in their water] for many, many years as well as reading and posting in bird sites and I have never heard such a thing. I know exactly how much water my birds drink. It depends on the species but they all have pretty much a set number of gulps and they all do it early in the morning and, sometimes, in the evening too. They are all prey animals so they are all crepuscular feeders and drinkers and, as such, are 'programmed' to drink at those times. Of course, if you feed your bird a diet that is nowhere near what nature meant for them to eat in terms of moisture [like pellets, for example], you will create an imbalance with the water intake but, usually, what happens is that the bird continues drinking pretty much the same amount it would drink if it was eating a 'normal' diet [meaning a wet one as they would do in the wild] and they end up have chronic mild dehydration all their lives which ends up affecting their kidneys and liver. And then there are the very smart ones that dunk all their dry food in the water.
Vitamins in the water are used exclusively with passerines because they are natural seed-eaters and do not normally consume soft -wet- food. Same thing with antibiotics or any other kind of medicine for them. It's pretty much the only way with passerines and it works perfectly [I've kept canaries for 50 years and have never had a single one develop a deficiency using the water method].
I use a powdered vitamin/mineral supplement in the gloop for the parrots but, when I first get a bird that has not been on a good diet, I use the ones in the water that I use for the canaries, finches, quails and cardinal because it takes too long to transition a parrot to a good diet and I want to 'replenish' the bird as soon as possible. I do this for a few weeks [it goes from two weeks to a couple of months, depending on the age, the length of time it has been on a bad diet and the health condition of the bird when I first get it] and then I start mixing the other kind in the gloop.
You can mix the vitamins with the soft food but, in all honesty, with new birds I find it easier to use the water soluble one in terms of accuracy of dosage because the vit/min supplements that go on the food are never specific as to the actual dose [they all tell you to sprinkle them on a pound of food or something like that but what, exactly, is a 'sprinkle'? a teaspoonful? half a teaspoonful? a quarter of a teaspoonful? an eight?] but the water soluble ones are very accurate: mine is half a teaspoonful in a gallon of water daily.
But, yes, by all means, put it on the soft food. And, yes, if the bird doesn't get stressed out by the spray bath, go ahead and do it - but use plain water, not any commercial spray.