If utility transformer center tap (neutral) bonds to ground, and you route Ground, L1 and L2 but not Neutral to your inverter & auto transformer, and if auto transformer has center tap bonded to ground ...
Then yes, current flows in the ground wire. Because neutral created by each transformer is not exactly midpoint between L1 and L2, depends on loading on each phase.
Do you have a residual current meter? How much current is flowing in ground?
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If you did feed your inverter and auto transformer with a 5 mA GFIC, it would probably trip.
So no particular qualification to evaluate safety of utility grid connected circuits.
Just like a whole lot of us who have an EE degree from an ABET approved institution/program.
An "EE" who is "professional" in the sense he gets paid for it. But not a "license professional engineer" recognized as an authority by the state.
Not that "UL Listed" or "Signed by a PE" is either necessary or sufficient for something to be safe. But it is accepted as an authoritative indication.
If you do have a ground wire between utility entrance and chassis of inverter etc., that is much safer.
A vendor provided a schematic lacking that, for use in U.S., and I think that carried serious risks.