sorry but I think you are misjudging just how much you learn both grammar and vocabulary from speaking a language natively and possibly misjudging how well education can teach someone a language
languages are these surprisingly complex and irregular things, which are way easier to learn by doing than by trying. often entering school you can already use tenses or grammatical structures that students learning English as a second language will struggle with a few years later in their educational journey, while you can spend that time unknowingly building up an even better subconscious understanding of the language.
Besides, from my experience, having basic Polish and extended English mind you, the tasks you are expected to do in the lessons of ones native language require a way higher degree of mastery than those in the second language of a pupil.
Also, it should be noted that non native speakers, or fluent speakers of multiple languages, can often borrow things from another language into English, either translating fraises literary (ex. once in a Russian year instead of once per blue moon) or using a unrelated word which happens to have a connection in the other language for other reasons (ex. castle and zipper both translate to "zamek" in Polish)
also mind that for a not insignificant number of people, though due to how more connected our world is today this has slightly decreased in the recent years, the level of English they ended up with from school is quite poor.