AC doesn’t work after lithium/inverter install

Going back to an earlier post you mention a toaster oven “ramping up” its power use. That doesn’t make sense. A resistive device will instantly go to full power and then actually fall just a bit as the elements heat. The ramping effect you are seeing may be a problem with your inverter or battery system limiting power on initial demand and could be the source of the air conditioner problem as well.