Replace the GFCI and see if that helps. Start with the CB panel knowing that the problem can be upstream. All circuit CBs off, disconnect all neutrals, leave all grounts connected. Does connecting any neutral cause the problem?
With all neutrals disconnected and utility power unplugged, inverter off ohm the neutral to ground which should be open. You might have something miswired conneting them together or an appliance that connects the neutral and ground.
Next step is to disconnect all neutrals and grounds and isolate which circuit is causing the problem. It can be multiple circuits such that the accumulated leak exceeds 5mA.
A light or something else that connects the hot to ground or neutral to ground can trip a GFCI.
What's upstream? ATS, EMC etc