The fact you speak more definitively in a formal setting, and the fact "going to" is informal (or not) are 2 different things. Cambridge dictionary is correct in that "going to" is used in more informal setting. It's that YOU are reading it wrong. It is not an informal expression. And by the way, some people take being proficient in one language not being in another, but they can actually co-exist. I write more in English than Japanese. Have been for over 10 years.