The house I'd love and the reality of what I can afford are leagues apart.
I lived in a house with a heavily terraced garden when my elder DC were young. We had a massive lawned area at the bottom with a river winding round it but mostly the adults sat on the top deck and children had their little level. It was great for trundle bikes and trikes without getting your ankles bashed. Good for paddling pool observation from above without getting soaked. Good for them burning off steam whilst barbequing. Also kept the child related colourful plastic in one area and the upper area was a calmer more designed space.
It required a little creativity for ball play but a drilled hole works well for swing ball - theres a football version of it too. The same hole works well for a rotary airer which again is nice to have on another level so you can enjoy sitting out without feeling like you're in a laundry.
We had a slide between levels - I can't see the height difference but you could potentially remove a section of the upper wall and put a bar across the top then have a slide down to the lower level.
We have a big pile of rubber floor tiles that have moved between 5 houses now. Originally down in a play room floor, they moved under a swing set, in a play house, as paths and in a greenhouse. Relatively cheep can be colourful or plain and a great play surface for whilst their little and you're thinking about what you want to do longer term.
That lower level without the shed is quite a good size. I wonder if there's potential to remove the front of the shed and have it as a big covered play area - plus somewhere to throw everything undercover when play is done.
Plenty of room for a pretend kitchen, swing, slide etc.
You could even have a little play cottage at the top with something querky like a firemans pole out the back to take your little energy bundles down to the bottom level.
The interior space is pretty good the cost per square foot for the area is good and potentially there's a bit more room for negotiation on the price. The big thing for me is its very livable. Nothing would have to be done on the surface of it to move in. You could do things one space at a time.