Most of the charts I've seen are very confusing. I think one reason is the temperature and cable length have big effects on capacity.
Here is the best site I've found so far. It even has a calculator for determining voltage drop.
https://www.powerstream.com/Wire_Size.htm
For short inverter wires, you want to use the "Chassis Wiring" amperage, not the "Power Transmission" amperage, which is for long runs through conduits, etc.
Pure Sine Wave inverters have an efficiency of between 90%-95%. So taking 90% as the worst case scenario, you want to take your max output of the inverter in watts, divide by .9, then divide by 12 to get the 12 v amperage at full load.
So taking your 3000 watt peak inverter that would be 277.8 amps at peak "Surge Power". Max chassis wiring amps for 00 AWG is 283, so that works out just right for 00 AWG cables and your inverter.
Now working backwards for 2 AWG cables, 81 max chassis wiring amps gives a capacity of 1955 watts. That's higher than your "Continuous Power" rating, so for most purposes that would probably be fine. But something like a big compressor motor at startup (which is what the "Surge Power" rating is for) could shut down your inverter using 2 AWG cables.