BALKAN-SL 2021 A2

Find all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ such that

$$f\left(x^{2}+y\right) \geqslant\left(\frac{1}{x}+1\right) f(y)$$

holds for all $x \in \mathbb{R} \backslash\{0\}$ and all $y \in \mathbb{R}$.