mobility scooters are not particularly heavy,
though I would recommend an additional sheet of ply be placed on the floor of the shed,
screwed to the shed floor bearers.
as the shed would cover the extended patio, you could simply lay a concrete pad,
over compacted hardcore.
or you could have the patio extended to match existing.
consider purchasing a shed with double doors for easy access.
you will probably need to have a small ramp too.
I hope this is useful to you.