Suppose that f is a function f: \mathbb{R}_{\geq 0} \rightarrow \mathbb{R} so that for all x, y \in \mathbb{R}_{>0} (nonnegative reals) we have that f(x)+f(y)=f(x+y+x y)+f(x) f(y). Given that f\left(\frac{3}{5}\right)=\frac{1}{2} and f(1)=3, determine \left\lfloor\log _{2}\left(-f\left(10^{2021}-1\right)\right)\right\rfloor.