I’m looking at doing trying something like this soon.
I would keep the filters in at least to filter derbies floating around.
Let me know how your project works out

Fish effluent does not contain all the nutrients the plants need, but if you use a soil like media (I use a blend of perlite and peat moss) you can introduce earthworms, and use limited amounts of nutrients to supplement the stuff coming from the fish. Fish effluent is mostly a source of nitrogen fertilizer, once naturally occurring soil bacteria break down the urea. Most states have extension agencies that will test your soil for free and recommend what you need to add.

Organic nutrients for plants primarily means no pesticides or drugs applied. Since plants, along with their symbiont bacteria and fungi, convert inorganic raw materials into biological/organic form. Most fertilizers and soil additives for enhancing plant growth are both non organic and perfectly safe to use. In some cases you may want to add additional nutrients. Iron, calcium and potassium, for example, are minerals typically missing in the water of aquaponic systems that would need to be added. I read one article that suggested you add nitrogen, which shows complete ignorance I think on the part of the author because nitrogen is the primarily constituent of fish effluent.

I am not sufficiently expert to give you much more than some general ideas about what should be added. I suggest googling aquaponic nutrient additives and doing some research. There are several styles of hydroponic systems you could adapt to aqyuaponics; continuous flow, flood and drain, and flotation for example and each method will have somewhat different requirements. What plants you raise and what kind of fish/crustacean will influence what you have to add to the water to create an optimal, balanced system. Figure out what you will be growing and raising and what kind of system you will have and then research what’s needed for that specifically. There are a number of forums on aquaponics where you could ask more experienced experts for specifics