You can run a ground wire from the inverter grounding screw to earth if necessary. I know the 12V ground is not sufficient to charge a car with the OEM charger.
I was told roughly the same thing your dealer told you, and they also told me that they would not do the update proactively, but only after codes were thrown. So I contacted a different dealer and mentioned service bulletin #24-NA-200 which you can read in full at...
And there is warranty language in the service bulletin. Regardless, my local dealer just told me that they won't do the update unless codes are thrown.
I'm curious to know how you tap into the traction battery.
The 12V battery gets replenished by the traction battery. According to Chevrolet, the maximum rate is 1600 watts, which is good for running most all of your 120V appliances, 1 at a time, for days.
That's helpful but I'm still confused. This Supercharger closest to me was installed this year: https://www.plugshare.com/location/543292 . According to plugshare, it's 250kw and V3, but according to the photos you linked, it's V2.