What you are describing is similar to Freshwater Aqua Culture and Aquaponics. It is a sophisticated, expensive operation which utilizing processes to remove solid wastes, oxidize toxic ammonia and oxyginate the water continously to prevent rotting.
If you are using this system it will be tatally organic Hydroponics.
You need to add autorophic bacteria to the growing medium so they can oxidize nitrite and ammonia to nitrate which plant can use. I would use an Ebb and Flow system with a submerging pump and a timer.
Give it a try and start with an easy plant to grow such as Lettuce or Basil. Good luck. Please let us know who it is progressing.
Safwat

I grow in an aero system and also keep worms and have experimented with using the tea mixed with liquid nutrients.

If you use the worm/compost tea without killing the organisms in the tea before you use it, your plumbing will get plugged up.

It made no measurable difference from just nutrient use with chiles.

It makes a huge difference in soil which is where I now put my tea.

Worm tea works fine for Hydroponic systems as a fully certifiable organic fertilizer and will not plug up your plumbing if larger liquid discharge orifices are used. Therefore, it is not suitable for aeroponics (which uses emitters to mist the roots with the hydroponic solution), but is ideal for most other forms of hydroponics. Perlite, which is very inexpensive in bulk ($8/5 cu ft from Perlite of Texas in San Antonio) has capillary active properties which are not commonly discussed, whereby liquids are "wicked" several inches through this grow medium, making it a contender for hydroponics growth medium. I have used it for decades and the only down side I have found is that of root buildup in the perlite. Depending on the design of your system, this could be a non-issue.