not using generator....inverter/battery instead
Seems like this use case is power back up. I believe that EG-4 product is relatively new. I have a bunch of their lower kW inverters and I run them in split phase. I understand you've got a grid feed on it - that purpose is to usually charge batteries, although it can be used (at least on mine) as pass-thru downstream.
How well that is going to work for a backup depends on your battery capacity... Looks like you have that covered with 3 batteries.
You cannot trust solar to power ****, you have to buffer to battery storage. Why? Because a single cloud can drop your power by 90%.
It is, to some degree, an ATS itself if you can isolate the load downstream. I think you've figured that out, interesting to loop it back to an interlock - it won't be automatic, but that should work.
Grounding is usually done within the inverter - EG-4 products (recently) have a config setting. I defer to Signature on it.
Watch EG-4's "idle draw" if you are going to depend on it. Idle draw can be quite high on these.