If you don’t want it to collapse then it needs to be built on a foundation built per the building code on concrete footings below the frost depth specified for your area again per the building code.

I don't know the building codes in the area where the OP lives. I live in Eastern North Carolina and you can build a building no more than 10' X 12' on skids with out a permit. (also no electricity or other utilities.)

SO If the building regulations permit, and you can position the building so the bumps and ruts do not interfere with the building, you can put a shed in that position.

If you can go this way, you would fist level the skids (4 x 4" or 6 X6'), and then lay the floor joist on the skids, Once the floor is secure, you would build the shed as you would any other building.

Great, I’ll look into this. Thank you. It’s only going to be 7x8’ so it’s fairly small

The structure appears to be a detached garage. Odds are it's a floating slab but it could have frost footings, so why does it matter? You need to build the foundation to whatever is under the garage.

If it's floating then the floor for the shed should be floating. If it has frost footings deep into the ground then the shed should also be the same and you don't want to mix the two. I don't see why you'd want to use any of the old heaved up concrete already there but who cares. About the code....yeah right. For a 7'x 8' bump out off the side of detached garage don't even bother messing with the city, just do it.

I am sorry I did not read the word "Lean To". If it is going to be part of the garage (Attached) then it needs the same foundation as is under the garage. If they are different the attached area will eventually pull a way from the garage proper.

One comment on a lean to arrangement. Coming out 7 or 8' is going to create an area between the fence and the attachment that will always be a problem area for anything you plant there.

One other comment, Since it appears you have a spacial problem, and since you are going to have to reproduce the garage foundation, have you though about just extending the wall out 7 or 8 feet for the length of the garage? You are going to have to get some equipment to break up the slabs that are there and dig the new foundation. I suspect the cost while more would not be that much more considering the extra space you will have for storage. Since you are embarking on large project that will tear up your yard, you may as well get the extra space.

I could be wrong, but it seems like if you want the structure to last, you need to put in the work to remove the existing uneven cement and pour new cement. If the slabs are already moving, they will likely continue to move. That said, even if you re-pour, if the tree is still in place and roots are close enough to the surface to damage the original concrete, I imagine it could happen with new concrete as well. You will need a floor for the shed anyway and it looks like right now 1/3 of the outlined space is just grass.