Boxes need to be grounded with wires (typically green for U.S.) to terminal lug, sheet metal screwed into metal case. Metal conduit between boxes does not qualify as grounding two boxes together because their threaded collar clamping rings often become loose, potentially making poor connection.
Think about consequences not grounding separated electrical metal boxes together. Left hand on one metal box, right hand on another metal box. Do you feel lucky or confident?
Grounding together metal electrical boxes is for safety and should be non-negotiable, but it is not going to solve any neutral to ground bonding issue that it might create with your inverter due to the single point ground to neutral bonding in main panel. Actual outside ground rod connection should only go to one point which is normally main input breaker panel.
Neutral should be brought back to single point neutral-ground bonded neutral bus bar in breaker box (typically main box). If you make any additional neutral to ground bonding in downstream boxes then you can have neutral return currents being shared on ground wires, which is a no-no, also creating a safety issue.