For many reasons ( nutrients, maintenance, testing, matching parameters for moving corals, etc.) I would find a way to plumb the frag tank to the display. Even if that means drilling a hole somewhere…
But if you are set on 2 separate systems, I second the biggest issue is lack of nutrients. I kept a coral only nano for a while, feeding reef roids every few days. And supplemented liquid nitrates and phosphates as needed. Some things grew, some just “survived”, and some died. When I ended up with 2 extra clowns and added them to the tank, the corals really came to life. Fish poop and Kalkawasser are unicorn juice.