I’m just redesigning our current garden, did the same with the last house. Here are some tips I found helpful.
Draw a birds-eye picture. Mark what you can’t move. Mark where the sun goes.
Write a list of essentials and desirables eg seating in morning, kids play. Look at the sun and mark where they could go.
Mark on paths. They have to go relatively straight or you’ll end up cutting the corner. If you want curved paths then block the way with plants etc.
You can mark out the design with your current planters to get an idea of how it would work in practice for walking around / sun etc.
Buying paving or decking is expensive. Look into lifting the existing paving and re-laying in a different shape, or rearranging to form paths etc.
We’re about to put in a pergola. If you do, make sure it will provide enough shade- the sun never goes directly overhead in the UK so you could find that half of the area underneath stays sunny. Use a stick’s shadow to check the shade area.
For plants put redder plants nearby and blues further away to make the garden look longer. That’s what light naturally does, like mountains far away look blue.
How about changing the shape to a backwards “C”? Curve the patio inside the angle of the L. Make a path at the end so you walk around the backwards C to the hut. Have a plant area from the hedge sweeping out to the centre and back. Fill the middle with grasses and soft plants, put shade loving wild flowers under the hedge. Hide the trampoline and goal at the tip of the C where they are now.