Wow! Amazing picks and an amazing garden! You have quite the green thumb. Shade tolerant stuff includes greens like spinach, miner's lettuce, French sorrel, kale, green onions, and baby greens. Many vines tolerate some shade but may drop some production if you are going for fruit because most things flower the most in sun. So like sweet potato, new zealand spinach, or Malabar spinach, might work in the shade since you don't eat the fruit on those. In your photos the shade doesn't look that dense. And, I agree, kids need watering from time to time.
I have recently stumbled upon https://4naturesystem.com and seen standers for plants. I think it might be good for herbs as well, although I have seen on their site vertical gardens mostly in office space. The plant stands have automatic irrigation so if you don’t have that much experience with gardening it could be easier for you to start.