You may have a hard time physically getting the lights close enough to the seedling(s) in a space bucket due to their shape and size. Basil, mint etc require much less light so that may work. You should do a few 2 week microgreen grows as an experiment just on a table or something (I grow microgreens in space buckets).

I personally use General Hydroponics Flora 3 part but it is similar to Fox Farms:

https://www.amazon.com/General-Hydroponics-Flora-Bloom-Fertilizer/dp/B01I4U0M32?th=1

I also use pH up (potassium hydroxide) and measure the pH with a 15 foot roll of pH paper:

https://www.google.com/search?q=General+Hydroponics+pH+Up&rlz=1CAVARX_enUS1044US1044&sourceid=chrome&ie=UTF-8

https://www.amazon.com/Micro-Essential-pHydrion-dispenser-5-5-8-0/dp/B0001SR4NM/ref=sr_1_3?keywords=phydrion&qid=1683657547&sr=8-3

I measure the water runoff from the soil for TDS and pH and fertilize appropriately but yes, I usually water with hydroponic solution when I add water to the soil (but my soil has almost no time release nutes and soil choice is important).