running underground electric service to shed on concrete slab
If you decide to use EMT in ground it will need to be buried 18” per NEC table 300.5.
You can bring the EMT up through the slab and bottom plate if you want . I bring conduit into buildings this way quite often. Make sure to allow for your disconnect many jurisdictions require it on the exterior of the structure.
You can bring the conduit up just outside the structure.
EMT coming through concrete is ok per NEC 358.10.B.1
My recommendation would be to run pvc underground and schedule 80 when you come up through the slab if not inside a wall, inside a wall schedule 40.
why pvc? Emt even though it is galvanized will rust out and EMT / concrete / earth although allowed sets up the ideal conditions to rust out so it will not last as long as PVC.  I have had rigid that I installed rust out but I have been doing this since the 70’s.