I agree, the 'as implemented' has big loops in the neutral circuit that should not be there. However, the line between the ground bus and neutral bus is, in NEC parlance, the Main Bonding Jumper and is appropriate. It is the neutral connection between the Grounding busbar in the Main panel and the Neutral Bus in the critical loads panel that is concerning (and I think should be removed).
View attachment 60420
However, I would not want to run the system without the inverter tied into the ground system.
It would be helpful to know more about the auto xfer switch. (Does it switch neutral or does it only switch the two hots?)