Hydroponics using just energy and (sea?) water

So you can make Ammonia (NH3) by taking water molecules, splitting it into H2 and O2 via hydrolisisers, and then using a plasma (or the Haber Bosch technique) to combine the H2 with Nitrogen from the air to produce Ammonia (NH3). Then there are bacteria which consume NH3 and produce NO2, and another bacteria which consume NO2 and produces NO3, which is Nitrate (these are the bacteria that are present in all fish tanks). Nitrate is the fertaliser that generates green leafy growth in plants, which we’ve manufactured with water + energy (basically). Could you use this as a basis of growing food from literally water and energy? Potassium & phosphorous are going to be impossible to manufacture from such simple inputs, but are arguably less important for green leafy plants. I also wonder how much K & P is in sea water & whether we can refine sea water to get all the things we need to grow a plant. I mean the proof is in the pudding really: Kelp. It should all be there if we can access and refine it using energy.