Not sure if anything is actually needed. It just looks unstable. Power is already run to the shed, so it might be difficult to move and do a full concrete pour. I was thinking of lifting with a car jack and finding a better combination of pavers to remove the wood wedges, but I'm open to any ideas. And it is on a slope, the other end is on pavers on the ground. This stack of pavers was the previous owners attempt at levelling I guess.
I would go with your first idea and jack it up. You could then dig out and pour some footings just on the 4 corners and the middle of the longest sides. Once you have the pads poured you can run 6x6 beams and have them rest on the concrete pads and lower the shed onto the beams.