Wiring generator to shed panel
You only have one choice here

Your generator has a bonded neutral, according to the manual I was able to find for it online, and I also could not find any instructions for removing that internal neutral-ground bond.  The bonded neutral is all well and good, and in fact the way it must be configured for standalone use, but this means that if you are using it to power up a structure, you will need to separate neutrals and grounds within the structure's panel, as if it were a subpanel.

As a result of this, you must go to a supply house or hardware store, get a Square-D PK7GTA ground bar kit, and fit it to your panel, as well as pulling the green bonding screw out of the panel in your shed.  You will then wire up the inlet as a four-wire connection with neutral to the neutral bar and ground to the ground bar; likewise, all ground wires that are currently terminated on the neutral bar will need to be moved to the ground bar.