I have the predecessor model, the EF2400iS. Yours has a higher start capacity than mine.
I have no problems running my Dometic 13,500 BTU A/C unit with other small appliances running.
But let me show you why this is a difficult task for even a 3000W generator.
The average ammeter is too slow to measure actual startup current. The spike happens very quickly, and it's difficult to get the compressor turning.
It takes just over a 50A spike to start my A/C. But the current immediately drops off to 10.5A afterwards.
Can't run the microwave or wife's hair dryer at the same time. But TV, lights, etc., no problem.
FWIW, the Yamaha 2400 series uses the same sized motor as the 2800W and 3000W models. This is why it can do the job, where others of a similar size can't.
Had this generator 13 years, used it at home, while traveling with the TT, and for days at my father's house on the mainland when we had to evacuate for hurricanes. Really is an excellent product.