A couple of late comments;
The 3 K EG4 inverter appears to come with a 125 Amp breaker, and the manual shows this breaker being connected to the positive battery input to the inverter.
A 125 amp breaker is sufficiently sized to protect #4 AWG cable, in free air, at 75 degrees C. Could not find any reference to the OP using such a breaker, or any other, at the input to the inverter.
The placement of a breaker at the input to the inverter would be customary, an most any battery-connected inverter, that I've seen.
There had been a question or two for a diagram, or pic on the layout of this system, but might have missed them, but did not see them.
See quite a lot of examples of just how simple and easy it is to hook u and use these AIO systems, and, more recently, there seems to be more focus on OCPDS in these setups on YT, but, it does appear that a number of users kind of tend to want to fudge on the specs of these AIO systems. IMO, probably all of the specs that have been fudged-on were done at the design and production phase of making these systems. Think that there is nothing in the way of specs that can be fudged, is left for more fudging.
Am a newbie on this fourm, so, it is not really my place to say anything about this ... but, just a thought.
FWIW 'Luke'