Does this simple omlette has that much fat like the recipe calculator said?

Yes, that is a lot of butter. I would use half the amount, and fry the veggies in it first til soft then just add the eggs to the same pan so the veggies are embedded in the omelette. That would be the usual way of doing it, I have never heard of frying them separately and putting them onm top, that sounds like extra faff!