EGMO 2021 Problem 2

Find all functions $f: \mathbb{Q} \rightarrow \mathbb{Q}$ such that the equation

$$f(x f(x)+y)=f(y)+x^{2}$$

holds for all rational numbers $x$ and $y$. Here, $\mathbb{Q}$ denotes the set of rational numbers. (Slovakia, Patrik Bak)