Bi-Lipschitz invariance of degree at infinity for complex algebraic sets

Let $X\subset\mathbb{C}^n$ and $Y\subset\mathbb{C}^m$ be two complex algebraic sets with

$$\dim X=\dim Y=d.$$

Degree-at-infinity conjecture. If $X$ and $Y$ are bi-Lipschitz homeomorphic at infinity, then

$$\operatorname{deg}(X)=\operatorname{deg}(Y).$$

This conjecture asks whether degree is preserved by bi-Lipschitz equivalence outside compact subsets. The source says that invariance of degree remains open, notably for affine hypersurfaces in $\mathbb{C}^n$ with $n>3$, although several special cases are known.