Don’t overthink it is all I would say as it sounds like a typical 3-year-old both of mine at that age were fussy eaters, we also did the extra meals thing as we wanted them to eat something, just remember they are only young and trying to get them to eat an adult meal may not be their idea of fun.
Mine are now 16 & 13 with incredible appetites and will eat anything and everything if given the chance.
In fact, we all went out Sat Night for a Thai meal in Leeds and if you had asked me 10 years ago during the fussy eating stage if that would happen I’d have told you NO!
Just be positive and offer different types of food but maybe not whilst having the family dinner and see how they get on.